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numbers</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="52232890" href="https://independent.academia.edu/KevinDjepang"><img alt="Profile image of Kevin Djepang" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/52232890/31297907/28790810/s65_kevin.djepang.jpg" />Kevin Djepang</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2014, Journal of Statistical Mechanics: Theory and Experiment</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":67055127,"attachmentType":"pdf","workUrl":"https://www.academia.edu/48449807/Site_percolation_on_lattices_with_low_average_coordination_numbers"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" 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class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/61558443/Size_distribution_of_percolating_clusters_on_cubic_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="6" data-entity-id="116085325" 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/116085325/Percolation_in_lattice_k_neighbor_graphs">Percolation in lattice $k$-neighbor graphs</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="49709354" href="https://bme.academia.edu/Andr%C3%A1sT%C3%B3bi%C3%A1s">András Tóbiás</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 2023</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":"Percolation in lattice $k$-neighbor graphs","attachmentId":112313333,"attachmentType":"pdf","work_url":"https://www.academia.edu/116085325/Percolation_in_lattice_k_neighbor_graphs","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/116085325/Percolation_in_lattice_k_neighbor_graphs"><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="22106521" 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/22106521/Percolation_on_two_and_three_dimensional_lattices">Percolation on two- and three-dimensional 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="43414141" href="https://independent.academia.edu/JPlascak">J. Plascak</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical review. E, Statistical, nonlinear, and soft matter physics, 2003</p><p class="ds-related-work--abstract ds2-5-body-sm">In this work we apply a highly efficient Monte Carlo algorithm recently proposed by Newman and Ziff to treat percolation problems. The site and bond percolations are studied on a number of lattices in two and three dimensions. Quite good results for the wrapping probabilities, correlation length critical exponent, and critical concentration are obtained for the square, simple cubic, hexagonal close packed, and hexagonal lattices by using relatively small systems. We also confirm the universal aspect of the wrapping probabilities regarding site and bond dilution.</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":"Percolation on two- and three-dimensional lattices","attachmentId":42775430,"attachmentType":"pdf","work_url":"https://www.academia.edu/22106521/Percolation_on_two_and_three_dimensional_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/22106521/Percolation_on_two_and_three_dimensional_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="98050154" 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/98050154/Site_trimer_percolation_on_square_lattices">Site trimer percolation on square 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="126008217" href="https://independent.academia.edu/PauloCentres">Paulo Centres</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical review. E, Statistical, nonlinear, and soft matter physics, 2015</p><p class="ds-related-work--abstract ds2-5-body-sm">Percolation of site trimers (k-mers with k=3) is investigated in a detailed way making use of an analytical model based on renormalization techniques in this problem. Results are compared to those obtained here by means of extensive computer simulations. Five different deposition possibilities for site trimers are included according to shape and orientation of the depositing objects. Analytical results for the percolation threshold p_{c} are all close to 0.55, while numerical results show a slight dispersion around this value. A comparison with p_{c} values previously reported for monomers and dimers establishes the tendency of p_{c} to decrease as k increases. Critical exponent ν was also obtained both by analytical and numerical methods. Results for the latter give values very close to the expected value 4/3 showing that this percolation case corresponds to the universality class of random percolation.</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":"Site trimer percolation on square lattices","attachmentId":99507547,"attachmentType":"pdf","work_url":"https://www.academia.edu/98050154/Site_trimer_percolation_on_square_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/98050154/Site_trimer_percolation_on_square_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="9" data-entity-id="48351134" 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/48351134/Site_percolation_on_the_Penrose_rhomb_lattice">Site percolation on the Penrose rhomb lattice</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="282899" href="https://umich.academia.edu/RobertZiff">Robert Ziff</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica A: Statistical Mechanics and its Applications, 1999</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":"Site percolation on the Penrose rhomb lattice","attachmentId":67010071,"attachmentType":"pdf","work_url":"https://www.academia.edu/48351134/Site_percolation_on_the_Penrose_rhomb_lattice","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/48351134/Site_percolation_on_the_Penrose_rhomb_lattice"><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":67055127,"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":67055127,"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_67055127" 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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