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window.loswp.showSignupCaptcha = false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":82302025,"created_at":"2022-06-28T10:18:13.247-07:00","from_world_paper_id":209415989,"updated_at":"2024-11-23T03:08:48.757-08:00","_data":{"publisher":"Elsevier BV","grobid_abstract":"Hamiltonian cycles with bending rigidity are studied on the first three members of the fractal family obtained by generalization of the modified rectangular (MR) fractal lattice. This model is proposed to describe conformational and thermodynamic properties of a single semi-flexible ring polymer confined in a poor and disordered (e.g. crowded) solvent. Due to the competition between temperature and polymer stiffness, there is a possibility for the phase transition between molten globule and crystal phase of a polymer to occur. The partition function of the model in the thermodynamic limit is obtained and analyzed as a function of polymer stiffness parameter s (Boltzmann weight), which for semi-flexible polymers can take on values over the interval (0,1). Other quantities, such as persistence length, specific heat and entropy, are obtained numerically and presented graphically as functions of stiffness parameter s.","publication_date":"2011,,","publication_name":"Physica A: Statistical Mechanics and its Applications","grobid_abstract_attachment_id":"88055171"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Semi-flexible compact polymers on fractal lattices","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [15510184]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":88055171,"attachmentType":"pdf"}"><img alt="First page of “Semi-flexible compact polymers on fractal lattices”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/88055171/mini_magick20220628-23069-y12rn4.png?1656436834" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/assets/single_work_splash/adobe.icon-574afd46eb6b03a77a153a647fb47e30546f9215c0ee6a25df597a779717f9ef.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Semi-flexible compact polymers on fractal lattices</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="15510184" href="https://bg.academia.edu/SuncicaElezovicHadzic"><img alt="Profile image of Suncica Elezovic-Hadzic" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/15510184/7344608/8258770/s65_suncica.elezovic-hadzic.jpg" />Suncica Elezovic-Hadzic</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2011, Physica A: Statistical Mechanics and its Applications</p></div><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":88055171,"attachmentType":"pdf","workUrl":"https://www.academia.edu/82302025/Semi_flexible_compact_polymers_on_fractal_lattices"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":88055171,"attachmentType":"pdf","workUrl":"https://www.academia.edu/82302025/Semi_flexible_compact_polymers_on_fractal_lattices"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div></div><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-doc_id="88055171" data-landing_url="https://www.academia.edu/82302025/Semi_flexible_compact_polymers_on_fractal_lattices" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="89696369" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/89696369/Phase_transitions_for_polymers_on_fractal_lattices">Phase transitions for polymers on fractal lattices</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="48874348" href="https://independent.academia.edu/JVannimenus">J. Vannimenus</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica D: Nonlinear Phenomena, 1989</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Phase transitions for polymers on fractal lattices","attachmentId":93446415,"attachmentType":"pdf","work_url":"https://www.academia.edu/89696369/Phase_transitions_for_polymers_on_fractal_lattices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/89696369/Phase_transitions_for_polymers_on_fractal_lattices"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="82302039" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/82302039/Semi_flexible_compact_polymers_in_two_dimensional_nonhomogeneous_confinement">Semi-flexible compact polymers in two dimensional nonhomogeneous confinement</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="15510184" href="https://bg.academia.edu/SuncicaElezovicHadzic">Suncica Elezovic-Hadzic</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Physics A: Mathematical and Theoretical, 2019</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Semi-flexible compact polymers in two dimensional nonhomogeneous confinement","attachmentId":88055182,"attachmentType":"pdf","work_url":"https://www.academia.edu/82302039/Semi_flexible_compact_polymers_in_two_dimensional_nonhomogeneous_confinement","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/82302039/Semi_flexible_compact_polymers_in_two_dimensional_nonhomogeneous_confinement"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="8051730" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/8051730/A_model_of_compact_polymers_on_a_family_of_three_dimensional_fractal_lattices">A model of compact polymers on a family of three-dimensional fractal lattices</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="15510184" href="https://bg.academia.edu/SuncicaElezovicHadzic">Suncica Elezovic-Hadzic</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Statistical Mechanics-theory and Experiment, 2010</p><p class="ds-related-work--abstract ds2-5-body-sm">We study Hamiltonian walks (HWs) on the family of three-dimensional modified Sierpinski gasket fractals, as a model for compact polymers in nonhomogeneous media in three dimensions. Each member of this fractal family is labeled with an integer b >= 2. We apply an exact recursive method which allows for explicit enumeration of extremely long Hamiltonian walks of different types: closed and open, with end-points anywhere in the lattice, or with one or both ends fixed at the corner sites, as well as some Hamiltonian conformations consisting of two or three strands. Analyzing large sets of data obtained for b = 2, 3 and 4, we find that numbers ZN of Hamiltonian walks, on fractal lattice with N sites, for N\gg 1 behave as ZN ~ ωNμNσ. The leading term ωN is characterized by the value of the connectivity constant ω > 1, which depends on b, but not on the type of HW. In contrast to that, the stretched exponential term μNσ depends on the type of HW through the constant μ < 1, whereas the exponent σ is determined by b alone. For larger b values, using some general features of the applied recursive relations, without explicit enumeration of HWs, we argue that the asymptotical behavior of ZN should be the same, with σ = ln3/ln[b(b + 1)(b + 2)/6], valid for all b > 2. This differs from the formulae obtained recently for Hamiltonian walks on other fractal lattices, as well as from the formula expected for homogeneous lattices. We discuss the possible origins and implications of such a result.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A model of compact polymers on a family of three-dimensional fractal lattices","attachmentId":48239513,"attachmentType":"pdf","work_url":"https://www.academia.edu/8051730/A_model_of_compact_polymers_on_a_family_of_three_dimensional_fractal_lattices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/8051730/A_model_of_compact_polymers_on_a_family_of_three_dimensional_fractal_lattices"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="56103918" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/56103918/Fractal_and_statistical_properties_of_large_compact_polymers_a_computational_study">Fractal and statistical properties of large compact polymers: a computational study</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="695310" href="https://nyu.academia.edu/AlexanderGrosberg">Alexander Grosberg</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Polymer, 2004</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fractal and statistical properties of large compact polymers: a computational study","attachmentId":71654817,"attachmentType":"pdf","work_url":"https://www.academia.edu/56103918/Fractal_and_statistical_properties_of_large_compact_polymers_a_computational_study","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/56103918/Fractal_and_statistical_properties_of_large_compact_polymers_a_computational_study"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="100796731" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/100796731/Conformational_Properties_of_Polymers_Near_a_Fractal_Surface">Conformational Properties of Polymers Near a Fractal Surface</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="67950298" href="https://independent.academia.edu/ViktoriaBlavatska">Viktoria Blavatska</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physics Procedia, 2012</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Conformational Properties of Polymers Near a Fractal Surface","attachmentId":101516392,"attachmentType":"pdf","work_url":"https://www.academia.edu/100796731/Conformational_Properties_of_Polymers_Near_a_Fractal_Surface","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/100796731/Conformational_Properties_of_Polymers_Near_a_Fractal_Surface"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="23844310" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/23844310/Fractal_Aspects_in_Polymer_Science">Fractal Aspects in Polymer Science</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="46093219" href="https://independent.academia.edu/HelmutSchiessel">Helmut Schiessel</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Fractals, 1995</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fractal Aspects in Polymer Science","attachmentId":44240791,"attachmentType":"pdf","work_url":"https://www.academia.edu/23844310/Fractal_Aspects_in_Polymer_Science","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/23844310/Fractal_Aspects_in_Polymer_Science"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="8051728" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/8051728/Stiffness_dependence_of_critical_exponents_of_semiflexible_polymer_chains_situated_on_two_dimensional_compact_fractals">Stiffness dependence of critical exponents of semiflexible polymer chains situated on two-dimensional compact fractals</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="15510184" href="https://bg.academia.edu/SuncicaElezovicHadzic">Suncica Elezovic-Hadzic</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2009</p><p class="ds-related-work--abstract ds2-5-body-sm">We present an exact and Monte Carlo renormalization group (MCRG) study of semiflexible polymer chains on an infinite family of the plane-filling (PF) fractals. The fractals are compact, that is, their fractal dimension $d_f$ is equal to 2 for all members of the fractal family enumerated by the odd integer $b$ ($3\le b< \infty$). For various values of stiffness parameter $s$ of the chain, on the PF fractals (for $3\le b\le 9$) we calculate exactly the critical exponents $\nu$ (associated with the mean squared end-to-end distances of polymer chain) and $\gamma$ (associated with the total number of different polymer chains). In addition, we calculate $\nu$ and $\gamma$ through the MCRG approach for $b$ up to 201. Our results show that, for each particular $b$, critical exponents are stiffness dependent functions, in such a way that the stiffer polymer chains (with smaller values of $s$) display enlarged values of $\nu$, and diminished values of $\gamma$. On the other hand, for any specific $s$, the critical exponent $\nu$ monotonically decreases, whereas the critical exponent $\gamma$ monotonically increases, with the scaling parameter $b$. We reflect on a possible relevance of the criticality of semiflexible polymer chains on the PF family of fractals to the same problem on the regular Euclidean lattices.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Stiffness dependence of critical exponents of semiflexible polymer chains situated on two-dimensional compact fractals","attachmentId":34509329,"attachmentType":"pdf","work_url":"https://www.academia.edu/8051728/Stiffness_dependence_of_critical_exponents_of_semiflexible_polymer_chains_situated_on_two_dimensional_compact_fractals","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/8051728/Stiffness_dependence_of_critical_exponents_of_semiflexible_polymer_chains_situated_on_two_dimensional_compact_fractals"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="6443739" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/6443739/Surface_adsorption_and_the_collapse_transition_of_a_linear_polymer_chain_Some_exact_results_on_fractal_lattices">Surface adsorption and the collapse transition of a linear polymer chain: Some exact results on fractal lattices</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="10178912" href="https://independent.academia.edu/YashwantSingh2">Yashwant Singh</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 1993</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Surface adsorption and the collapse transition of a linear polymer chain: Some exact results on fractal lattices","attachmentId":48866911,"attachmentType":"pdf","work_url":"https://www.academia.edu/6443739/Surface_adsorption_and_the_collapse_transition_of_a_linear_polymer_chain_Some_exact_results_on_fractal_lattices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/6443739/Surface_adsorption_and_the_collapse_transition_of_a_linear_polymer_chain_Some_exact_results_on_fractal_lattices"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="23844311" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/23844311/On_the_stability_of_fractal_globules">On the stability of fractal globules</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="46093219" href="https://independent.academia.edu/HelmutSchiessel">Helmut Schiessel</a></div><p class="ds-related-work--metadata ds2-5-body-xs">The Journal of Chemical Physics, 2013</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the stability of fractal globules","attachmentId":44240807,"attachmentType":"pdf","work_url":"https://www.academia.edu/23844311/On_the_stability_of_fractal_globules","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/23844311/On_the_stability_of_fractal_globules"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="8051739" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/8051739/Interacting_linear_polymers_on_three_dimensional_Sierpinski_fractals">Interacting linear polymers on three-dimensional Sierpinski fractals</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="15510184" href="https://bg.academia.edu/SuncicaElezovicHadzic">Suncica Elezovic-Hadzic</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2002</p><p class="ds-related-work--abstract ds2-5-body-sm">Using self-avoiding walk model on three-dimensional Sierpinski fractals (3d SF) we have studied critical properties of self-interacting linear polymers in porous environment, via exact real-space renormalization group (RG) method. We have found that RG equations for 3d SF with base b=4 are much more complicated than for the previously studied b=2 and b=3 3d SFs. Numerical analysis of these equations shows that for all considered cases there are three fixed points, corresponding to the high-temperature extended polymer state, collapse transition, and the low-temperature state, which is compact or semi-compact, depending on the value of the fractal base b. We discuss the reasons for such different low--temperature behavior, as well as the possibility of establishing the RG equations beyond b=4.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Interacting linear polymers on three-dimensional Sierpinski fractals","attachmentId":34509343,"attachmentType":"pdf","work_url":"https://www.academia.edu/8051739/Interacting_linear_polymers_on_three_dimensional_Sierpinski_fractals","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/8051739/Interacting_linear_polymers_on_three_dimensional_Sierpinski_fractals"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":88055171,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":88055171,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_88055171" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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data-collection-position="5" data-entity-id="30655061" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/30655061/Polymers_with_self_attraction_and_stiffness_a_generic_phase_structure">Polymers with self-attraction and stiffness: a generic phase structure</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="15817" href="https://qmul.academia.edu/ThomasPrellberg">Thomas Prellberg</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Polymers with self-attraction and stiffness: a generic phase 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E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Multifractal behavior of linear polymers in disordered media","attachmentId":70788597,"attachmentType":"pdf","work_url":"https://www.academia.edu/54413788/Multifractal_behavior_of_linear_polymers_in_disordered_media","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/54413788/Multifractal_behavior_of_linear_polymers_in_disordered_media"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" 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data-collection-position="20" data-entity-id="79605279" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/79605279/Directed_polymers_on_fractal_substrates">Directed polymers on fractal substrates</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="137107136" href="https://independent.academia.edu/GertZumofen">Gert Zumofen</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review A, 1992</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Directed polymers on fractal substrates","attachmentId":86263029,"attachmentType":"pdf","work_url":"https://www.academia.edu/79605279/Directed_polymers_on_fractal_substrates","alternativeTracking":true}"><span 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