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</div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2312.11614">arXiv:2312.11614</a> <span> [<a href="https://arxiv.org/pdf/2312.11614">pdf</a>, <a href="https://arxiv.org/format/2312.11614">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> The Nordic-walking mechanism and its explanation of deconfined pseudocriticality from Wess-Zumino-Witten theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Hawashin%2C+B">Bilal Hawashin</a>, <a href="/search/cond-mat?searchtype=author&query=Eichhorn%2C+A">Astrid Eichhorn</a>, <a href="/search/cond-mat?searchtype=author&query=Janssen%2C+L">Lukas Janssen</a>, <a href="/search/cond-mat?searchtype=author&query=Scherer%2C+M+M">Michael M. Scherer</a>, <a href="/search/cond-mat?searchtype=author&query=Ray%2C+S">Shouryya Ray</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2312.11614v1-abstract-short" style="display: inline;"> The understanding of phenomena falling outside the Ginzburg-Landau paradigm of phase transitions represents a key challenge in condensed matter physics. A famous class of examples is constituted by the putative deconfined quantum critical points between two symmetry-broken phases in layered quantum magnets, such as pressurised SrCu$_2$(BO$_3$)$_2$. Experiments find a weak first-order transition, w… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.11614v1-abstract-full').style.display = 'inline'; document.getElementById('2312.11614v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2312.11614v1-abstract-full" style="display: none;"> The understanding of phenomena falling outside the Ginzburg-Landau paradigm of phase transitions represents a key challenge in condensed matter physics. A famous class of examples is constituted by the putative deconfined quantum critical points between two symmetry-broken phases in layered quantum magnets, such as pressurised SrCu$_2$(BO$_3$)$_2$. Experiments find a weak first-order transition, which simulations of relevant microscopic models can reproduce. The origin of this behaviour has been a matter of considerable debate for several years. In this work, we demonstrate that the nature of the deconfined quantum critical point can be best understood in terms of a novel dynamical mechanism, termed Nordic walking. Nordic walking denotes a renormalisation group flow arising from a beta function that is flat over a range of couplings. This gives rise to a logarithmic flow that is faster than the well-known walking behaviour, associated with the annihilation and complexification of fixed points, but still significantly slower than the generic running of couplings. The Nordic-walking mechanism can thus explain weak first-order transitions, but may also play a role in high-energy physics, where it could solve hierarchy problems. We analyse the Wess-Zumino-Witten field theory pertinent to deconfined quantum critical points with a topological term in 2+1 dimensions. To this end, we construct an advanced functional renormalisation group approach based on higher-order regulators. We thereby calculate the beta function directly in 2+1 dimensions and provide evidence for Nordic walking. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.11614v1-abstract-full').style.display = 'none'; document.getElementById('2312.11614v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 + 11 pages (typeset with sn-jnl.cls), 4 + 1 figures; comments welcome</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2107.07325">arXiv:2107.07325</a> <span> [<a href="https://arxiv.org/pdf/2107.07325">pdf</a>, <a href="https://arxiv.org/format/2107.07325">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Physics and Society">physics.soc-ph</span> </div> </div> <p class="title is-5 mathjax"> A sprinkling of hybrid-signature discrete spacetimes in real-world networks </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Eichhorn%2C+A">Astrid Eichhorn</a>, <a href="/search/cond-mat?searchtype=author&query=Pauly%2C+M">Martin Pauly</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2107.07325v1-abstract-short" style="display: inline;"> Many real-world networks are embedded into a space or spacetime. The embedding space(time) constrains the properties of these real-world networks. We use the scale-dependent spectral dimension as a tool to probe whether real-world networks encode information on the dimensionality of the embedding space. We find that spacetime networks which are inspired by quantum gravity and based on a hybrid sig… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.07325v1-abstract-full').style.display = 'inline'; document.getElementById('2107.07325v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2107.07325v1-abstract-full" style="display: none;"> Many real-world networks are embedded into a space or spacetime. The embedding space(time) constrains the properties of these real-world networks. We use the scale-dependent spectral dimension as a tool to probe whether real-world networks encode information on the dimensionality of the embedding space. We find that spacetime networks which are inspired by quantum gravity and based on a hybrid signature, following the Minkowski metric at small spatial distance and the Euclidean metric at large spatial distance, provide a template relevant for real-world networks of small-world type, including a representation of the internet's architecture and biological neural networks. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.07325v1-abstract-full').style.display = 'none'; document.getElementById('2107.07325v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 July, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">19 pages, 18 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2006.04853">arXiv:2006.04853</a> <span> [<a href="https://arxiv.org/pdf/2006.04853">pdf</a>, <a href="https://arxiv.org/format/2006.04853">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physrep.2021.01.001">10.1016/j.physrep.2021.01.001 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The nonperturbative functional renormalization group and its applications </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Dupuis%2C+N">N. Dupuis</a>, <a href="/search/cond-mat?searchtype=author&query=Canet%2C+L">L. Canet</a>, <a href="/search/cond-mat?searchtype=author&query=Eichhorn%2C+A">A. Eichhorn</a>, <a href="/search/cond-mat?searchtype=author&query=Metzner%2C+W">W. Metzner</a>, <a href="/search/cond-mat?searchtype=author&query=Pawlowski%2C+J+M">J. M. Pawlowski</a>, <a href="/search/cond-mat?searchtype=author&query=Tissier%2C+M">M. Tissier</a>, <a href="/search/cond-mat?searchtype=author&query=Wschebor%2C+N">N. Wschebor</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2006.04853v3-abstract-short" style="display: inline;"> The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for viable ultraviolet completions in fundamental physics. It provides us with a natural framework to study theoretical models where degrees of freedom are correlated o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2006.04853v3-abstract-full').style.display = 'inline'; document.getElementById('2006.04853v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2006.04853v3-abstract-full" style="display: none;"> The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for viable ultraviolet completions in fundamental physics. It provides us with a natural framework to study theoretical models where degrees of freedom are correlated over long distances and that may exhibit very distinct behavior on different energy scales. The nonperturbative functional renormalization-group (FRG) approach is a modern implementation of Wilson's RG, which allows one to set up nonperturbative approximation schemes that go beyond the standard perturbative RG approaches. The FRG is based on an exact functional flow equation of a coarse-grained effective action (or Gibbs free energy in the language of statistical mechanics). We review the main approximation schemes that are commonly used to solve this flow equation and discuss applications in equilibrium and out-of-equilibrium statistical physics, quantum many-particle systems, high-energy physics and quantum gravity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2006.04853v3-abstract-full').style.display = 'none'; document.getElementById('2006.04853v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 May, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 June, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v3) Review article, 93 pages + bibliography, 35 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physics Reports 910, 1 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1606.07449">arXiv:1606.07449</a> <span> [<a href="https://arxiv.org/pdf/1606.07449">pdf</a>, <a href="https://arxiv.org/format/1606.07449">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevE.94.042105">10.1103/PhysRevE.94.042105 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Universal behavior of coupled order parameters below three dimensions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Borchardt%2C+J">Julia Borchardt</a>, <a href="/search/cond-mat?searchtype=author&query=Eichhorn%2C+A">Astrid Eichhorn</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1606.07449v1-abstract-short" style="display: inline;"> We explore universal critical behavior in models with two competing order parameters, and an O(N)+O(M) symmetry for dimensions $d \leq 3$. In d=3, there is always exactly one stable Renormalization Group fixed point, corresponding to bicritical or tetracritical behavior. Employing novel, pseudo-spectral techniques to solve functional Renormalization Group equations in a two-dimensional field space… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1606.07449v1-abstract-full').style.display = 'inline'; document.getElementById('1606.07449v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1606.07449v1-abstract-full" style="display: none;"> We explore universal critical behavior in models with two competing order parameters, and an O(N)+O(M) symmetry for dimensions $d \leq 3$. In d=3, there is always exactly one stable Renormalization Group fixed point, corresponding to bicritical or tetracritical behavior. Employing novel, pseudo-spectral techniques to solve functional Renormalization Group equations in a two-dimensional field space, we uncover a more intricate structure of fixed points in d<3, where two additional bicritical fixed points play a role. Towards d=2, we discover ranges of N=M with several simultaneously stable fixed points, indicating the coexistence of several universality classes. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1606.07449v1-abstract-full').style.display = 'none'; document.getElementById('1606.07449v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 June, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">17 pages, 16 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. E 94, 042105 (2016) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1604.03561">arXiv:1604.03561</a> <span> [<a href="https://arxiv.org/pdf/1604.03561">pdf</a>, <a href="https://arxiv.org/format/1604.03561">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.93.125021">10.1103/PhysRevD.93.125021 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Critical O(N) models above four dimensions: Small-N solutions and stability </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Eichhorn%2C+A">Astrid Eichhorn</a>, <a href="/search/cond-mat?searchtype=author&query=Janssen%2C+L">Lukas Janssen</a>, <a href="/search/cond-mat?searchtype=author&query=Scherer%2C+M+M">Michael M. Scherer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1604.03561v1-abstract-short" style="display: inline;"> We explore O(N) models in dimensions $4<d<6$. Specifically, we investigate models of an O(N) vector field coupled to an additional scalar field via a cubic interaction. Recent results in $d=6-蔚$ have uncovered an interacting ultraviolet fixed point of the renormalization group (RG) if the number N of components of the vector field is large enough, suggesting that these models are asymptotically sa… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1604.03561v1-abstract-full').style.display = 'inline'; document.getElementById('1604.03561v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1604.03561v1-abstract-full" style="display: none;"> We explore O(N) models in dimensions $4<d<6$. Specifically, we investigate models of an O(N) vector field coupled to an additional scalar field via a cubic interaction. Recent results in $d=6-蔚$ have uncovered an interacting ultraviolet fixed point of the renormalization group (RG) if the number N of components of the vector field is large enough, suggesting that these models are asymptotically safe. We set up a functional RG analysis of these systems to address three key issues: Firstly, we find that in $d=5$ the interacting fixed point exists all the way down to N=1. Secondly, we show that the standard O(N) universality classes are actually embedded in those of the cubic models, in that the latter exhibit the same values for (most of) the critical exponents, but feature an additional third RG relevant direction. Thirdly, we address the critical question of global stability of the fixed-point potential to test whether the fixed point can underly a viable quantum field theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1604.03561v1-abstract-full').style.display = 'none'; document.getElementById('1604.03561v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 April, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, 12 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 93, 125021 (2016) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1510.04807">arXiv:1510.04807</a> <span> [<a href="https://arxiv.org/pdf/1510.04807">pdf</a>, <a href="https://arxiv.org/format/1510.04807">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1140/epjc/s10052-016-3921-3">10.1140/epjc/s10052-016-3921-3 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Discovering and quantifying nontrivial fixed points in multi-field models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Eichhorn%2C+A">Astrid Eichhorn</a>, <a href="/search/cond-mat?searchtype=author&query=Helfer%2C+T">Thomas Helfer</a>, <a href="/search/cond-mat?searchtype=author&query=Mesterh%C3%A1zy%2C+D">David Mesterh谩zy</a>, <a href="/search/cond-mat?searchtype=author&query=Scherer%2C+M+M">Michael M. Scherer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1510.04807v3-abstract-short" style="display: inline;"> We use the functional renormalization group and the $蔚$-expansion concertedly to explore multicritical universality classes for coupled $\bigoplus_i O(N_i)$ vector-field models in three Euclidean dimensions. Exploiting the complementary strengths of these two methods we show how to make progress in theories with large numbers of interactions, and a large number of possible symmetry-breaking patter… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1510.04807v3-abstract-full').style.display = 'inline'; document.getElementById('1510.04807v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1510.04807v3-abstract-full" style="display: none;"> We use the functional renormalization group and the $蔚$-expansion concertedly to explore multicritical universality classes for coupled $\bigoplus_i O(N_i)$ vector-field models in three Euclidean dimensions. Exploiting the complementary strengths of these two methods we show how to make progress in theories with large numbers of interactions, and a large number of possible symmetry-breaking patterns. For the three- and four-field models we find a new fixed point that arises from the mutual interaction between different field sectors, and we establish the absence of infrared-stable fixed point solutions for the regime of small $N_i$. Moreover, we explore these systems as toy models for theories that are both asymptotically safe and infrared complete. In particular, we show that these models exhibit complete renormalization group trajectories that begin and end at nontrivial fixed points. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1510.04807v3-abstract-full').style.display = 'none'; document.getElementById('1510.04807v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 March, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 October, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10 pages, 6 figures; minor changes, as published in EPJ C</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> The European Physical Journal C 76, 1 (2016) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1408.4127">arXiv:1408.4127</a> <span> [<a href="https://arxiv.org/pdf/1408.4127">pdf</a>, <a href="https://arxiv.org/format/1408.4127">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.90.104039">10.1103/PhysRevD.90.104039 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Eichhorn%2C+A">Astrid Eichhorn</a>, <a href="/search/cond-mat?searchtype=author&query=Koslowski%2C+T">Tim Koslowski</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1408.4127v2-abstract-short" style="display: inline;"> We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the analysis of [1], we study three new aspects of the double-scaling limit of matrix models as Renormalization Group fixed points: Firstly, we investigate multicritical… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1408.4127v2-abstract-full').style.display = 'inline'; document.getElementById('1408.4127v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1408.4127v2-abstract-full" style="display: none;"> We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the analysis of [1], we study three new aspects of the double-scaling limit of matrix models as Renormalization Group fixed points: Firstly, we investigate multicritical fixed points, which are associated with quantum gravity coupled to conformal matter. Secondly, we discuss an approximation that reduces the scheme dependence of our results as well as computational effort while giving good numerical results. This is a consequence of the approximation being a solution to the unitary Ward-identity associated to the U(N) symmetry of the hermitian matrix model. Thirdly, we discuss a scenario that relates the double scaling limit to fixed points of continuum quantum gravity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1408.4127v2-abstract-full').style.display = 'none'; document.getElementById('1408.4127v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 August, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 August, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages, 1 figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 90, 104039 (2014) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1407.7442">arXiv:1407.7442</a> <span> [<a href="https://arxiv.org/pdf/1407.7442">pdf</a>, <a href="https://arxiv.org/format/1407.7442">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevE.90.052129">10.1103/PhysRevE.90.052129 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Stability of fixed points and generalized critical behavior in multifield models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Eichhorn%2C+A">Astrid Eichhorn</a>, <a href="/search/cond-mat?searchtype=author&query=Mesterh%C3%A1zy%2C+D">David Mesterh谩zy</a>, <a href="/search/cond-mat?searchtype=author&query=Scherer%2C+M+M">Michael M. Scherer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1407.7442v2-abstract-short" style="display: inline;"> We study models with three coupled vector fields characterized by $O(N_1)\oplus O(N_2) \oplus O(N_3)$ symmetry. Using the nonperturbative functional renormalization group, we derive $尾$ functions for the couplings and anomalous dimensions in $d$ dimensions. Specializing to the case of three dimensions, we explore interacting fixed points that generalize the $O(N)$ Wilson-Fisher fixed point. We fin… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1407.7442v2-abstract-full').style.display = 'inline'; document.getElementById('1407.7442v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1407.7442v2-abstract-full" style="display: none;"> We study models with three coupled vector fields characterized by $O(N_1)\oplus O(N_2) \oplus O(N_3)$ symmetry. Using the nonperturbative functional renormalization group, we derive $尾$ functions for the couplings and anomalous dimensions in $d$ dimensions. Specializing to the case of three dimensions, we explore interacting fixed points that generalize the $O(N)$ Wilson-Fisher fixed point. We find a symmetry-enhanced isotropic fixed point, a large class of fixed points with partial symmetry enhancement, as well as partially and fully decoupled fixed point solutions. We discuss their stability properties for all values of $N_1, N_2$, and $N_3$, emphasizing important differences to the related two-field models. For small numbers of field components we find no stable fixed point solutions, and we argue that this can be attributed to the presence of a large class of possible (mixed) couplings in the three-field and multifield models. Furthermore, we contrast different mechanisms for stability interchange between fixed points in the case of the two- and three-field models, which generically proceed through fixed-point collisions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1407.7442v2-abstract-full').style.display = 'none'; document.getElementById('1407.7442v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 November, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 July, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages, 15 figures; PRE version, minor changes</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. E 90, 052129 (2014) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1306.2952">arXiv:1306.2952</a> <span> [<a href="https://arxiv.org/pdf/1306.2952">pdf</a>, <a href="https://arxiv.org/format/1306.2952">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevE.88.042141">10.1103/PhysRevE.88.042141 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Multicritical behavior in models with two competing order parameters </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Eichhorn%2C+A">Astrid Eichhorn</a>, <a href="/search/cond-mat?searchtype=author&query=Mesterh%C3%A1zy%2C+D">David Mesterh谩zy</a>, <a href="/search/cond-mat?searchtype=author&query=Scherer%2C+M+M">Michael M. Scherer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1306.2952v2-abstract-short" style="display: inline;"> We employ the nonperturbative functional Renormalization Group to study models with an O(N_1)+O(N_2) symmetry. Here, different fixed points exist in three dimensions, corresponding to bicritical and tetracritical behavior induced by the competition of two order parameters. We discuss the critical behavior of the symmetry-enhanced isotropic, the decoupled and the biconical fixed point, and analyze… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1306.2952v2-abstract-full').style.display = 'inline'; document.getElementById('1306.2952v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1306.2952v2-abstract-full" style="display: none;"> We employ the nonperturbative functional Renormalization Group to study models with an O(N_1)+O(N_2) symmetry. Here, different fixed points exist in three dimensions, corresponding to bicritical and tetracritical behavior induced by the competition of two order parameters. We discuss the critical behavior of the symmetry-enhanced isotropic, the decoupled and the biconical fixed point, and analyze their stability in the N_1, N_2 plane. We study the fate of non-trivial fixed points during the transition from three to four dimensions, finding evidence for a triviality problem for coupled two-scalar models in high-energy physics. We also point out the possibility of non-canonical critical exponents at semi-Gaussian fixed points and show the emergence of Goldstone modes from discrete symmetries. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1306.2952v2-abstract-full').style.display = 'none'; document.getElementById('1306.2952v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 October, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 June, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages, 7 figures, 5 tables, minor changes in updated version, identical to published one in Phys. Rev. E</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. E 88, 042141 (2013) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1304.7247">arXiv:1304.7247</a> <span> [<a href="https://arxiv.org/pdf/1304.7247">pdf</a>, <a href="https://arxiv.org/ps/1304.7247">ps</a>, <a href="https://arxiv.org/format/1304.7247">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.87.124028">10.1103/PhysRevD.87.124028 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Probing the quantum nature of spacetime by diffusion </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Calcagni%2C+G">Gianluca Calcagni</a>, <a href="/search/cond-mat?searchtype=author&query=Eichhorn%2C+A">Astrid Eichhorn</a>, <a href="/search/cond-mat?searchtype=author&query=Saueressig%2C+F">Frank Saueressig</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1304.7247v2-abstract-short" style="display: inline;"> Many approaches to quantum gravity have resorted to diffusion processes to characterize the spectral properties of the resulting quantum spacetimes. We critically discuss these quantum-improved diffusion equations and point out that a crucial property, namely positivity of their solutions, is not preserved automatically. We then construct a novel set of diffusion equations with positive semi-defin… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1304.7247v2-abstract-full').style.display = 'inline'; document.getElementById('1304.7247v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1304.7247v2-abstract-full" style="display: none;"> Many approaches to quantum gravity have resorted to diffusion processes to characterize the spectral properties of the resulting quantum spacetimes. We critically discuss these quantum-improved diffusion equations and point out that a crucial property, namely positivity of their solutions, is not preserved automatically. We then construct a novel set of diffusion equations with positive semi-definite probability densities, applicable to Asymptotically Safe gravity, Horava-Lifshitz gravity and Loop Quantum Gravity. These recover all previous results on the spectral dimension and shed further light on the structure of the quantum spacetimes by assessing the underlying stochastic processes. Pointing out that manifestly different diffusion processes lead to the same spectral dimension, we propose the probability distribution of the diffusion process as a refined probe of quantum spacetime. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1304.7247v2-abstract-full').style.display = 'none'; document.getElementById('1304.7247v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 June, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 April, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages, 5 figures; v2: minor typos corrected</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 87, 124028 (2013) </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div>  </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

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