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dc.contributor.authorCodello, A
dc.contributor.authorDrach, V
dc.contributor.authorHietanen, A
dc.date.accessioned2018-03-08T08:48:32Z
dc.date.available2018-03-08T08:48:32Z
dc.date.issued2015-11
dc.identifier.issn1742-5468
dc.identifier.issn1742-5468
dc.identifier.otherARTN P11008
dc.identifier.urihttp://hdl.handle.net/10026.1/11013
dc.description22 pages, 10 figures and 3 tables; v2: references added
dc.description.abstract

We construct periodic approximations to the free energies of Ising models on fractal lattices of dimension smaller than two, in the case of a zero external magnetic field, based on the combinatorial method of Feynman and Vdovichenko. We show that the procedure is applicable to any fractal obtained by the removal of sites from a periodic two-dimensional lattice. As a first application, we compute estimates for the critical temperatures of many different Sierpinski carpets and we compare them to known Monte Carlo estimates. The results show that our method is capable of determining the critical temperature with, possibly, arbitrary accuracy and paves the way for determination Tc of any fractal of dimension less than two. Critical exponents are more diffcult to determine since the free energy of any periodic approximation still has a logarithmic singularity at the critical point implying α = 0. We also compute the correlation length as a function of the temperature and extract the relative critical exponent. We find V = 1 for all periodic approximations, as expected from universality.

dc.format.extentP11008-P11008
dc.language.isoen
dc.publisherIOP Publishing
dc.subjectsolvable lattice models
dc.subjectclassical phase transitions (theory)
dc.subjectcritical exponents and amplitudes (theory)
dc.titleApproximating the Ising model on fractal lattices of dimension less than two
dc.typejournal-article
dc.typeJournal Article
plymouth.author-urlhttps://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000366681400009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=11bb513d99f797142bcfeffcc58ea008
plymouth.issue11
plymouth.volume2015
plymouth.publisher-urlhttp://dx.doi.org/10.1088/1742-5468/2015/11/P11008
plymouth.publication-statusPublished online
plymouth.journalJournal of Statistical Mechanics: Theory and Experiment
dc.identifier.doi10.1088/1742-5468/2015/11/p11008
plymouth.organisational-group/Plymouth
plymouth.organisational-group/Plymouth/Faculty of Science and Engineering
plymouth.organisational-group/Plymouth/REF 2021 Researchers by UoA
plymouth.organisational-group/Plymouth/REF 2021 Researchers by UoA/EXTENDED UoA 10 - Mathematical Sciences
plymouth.organisational-group/Plymouth/REF 2021 Researchers by UoA/UoA10 Mathematical Sciences
plymouth.organisational-group/Plymouth/Users by role
plymouth.organisational-group/Plymouth/Users by role/Academics
dc.identifier.eissn1742-5468
dc.rights.embargoperiodNot known
rioxxterms.versionofrecord10.1088/1742-5468/2015/11/p11008
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.typeJournal Article/Review


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