dc.contributor.author Codello, A en dc.contributor.author Drach, V en dc.contributor.author Hietanen, A en dc.date.accessioned 2018-03-08T08:48:32Z dc.date.available 2018-03-08T08:48:32Z dc.identifier.uri http://hdl.handle.net/10026.1/11013 dc.description 22 pages, 10 figures and 3 tables; v2: references added en 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 zero external magnetic field, using a generalization of the combinatorial method of Feynman and Vodvickenko. Our procedure is applicable to any fractal obtained by the removal of sites of 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 to determine $T_c$ for any fractal of dimension below two. Critical exponents are more difficult to determine since the free energy of any periodic approximation still has a logarithmic singularity at the critical point implying $\alpha = 0$. We also compute the correlation length as a function of the temperature and extract the relative critical exponent. We find $\nu=1$ for all periodic approximation, as expected from universality. en dc.language.iso en en dc.subject cond-mat.stat-mech en dc.subject cond-mat.stat-mech en dc.subject hep-lat en dc.title Approximating the Ising model on fractal lattices of dimension below two en dc.type Journal Article plymouth.author-url http://arxiv.org/abs/1505.02699v2 en plymouth.publisher-url http://dx.doi.org/10.1088/1742-5468/2015/11/P11008 en plymouth.journal J. Stat. Mech. (2015) P11008 en dc.identifier.doi 10.1088/1742-5468/2015/11/P11008 en plymouth.organisational-group /Plymouth plymouth.organisational-group /Plymouth/00 Groups by role plymouth.organisational-group /Plymouth/00 Groups by role/Academics plymouth.organisational-group /Plymouth/Faculty of Science and Engineering plymouth.organisational-group /Plymouth/Faculty of Science and Engineering/School of Computing, Electronics and Mathematics plymouth.organisational-group /Plymouth/REF 2021 Researchers by UoA plymouth.organisational-group /Plymouth/REF 2021 Researchers by UoA/UoA10 Mathematical Sciences dc.rights.embargoperiod Not known en rioxxterms.versionofrecord 10.1088/1742-5468/2015/11/P11008 en rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved en rioxxterms.type Journal Article/Review en
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