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dc.contributor.authorCodello, Aen
dc.contributor.authorDrach, Ven
dc.contributor.authorHietanen, Aen
dc.date.accessioned2018-03-08T08:48:32Z
dc.date.available2018-03-08T08:48:32Z
dc.identifier.urihttp://hdl.handle.net/10026.1/11013
dc.description22 pages, 10 figures and 3 tables; v2: references addeden
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.isoenen
dc.subjectcond-mat.stat-mechen
dc.subjectcond-mat.stat-mechen
dc.subjecthep-laten
dc.titleApproximating the Ising model on fractal lattices of dimension below twoen
dc.typeJournal Article
plymouth.author-urlhttp://arxiv.org/abs/1505.02699v2en
plymouth.publisher-urlhttp://dx.doi.org/10.1088/1742-5468/2015/11/P11008en
plymouth.journalJ. Stat. Mech. (2015) P11008en
dc.identifier.doi10.1088/1742-5468/2015/11/P11008en
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.embargoperiodNot knownen
rioxxterms.versionofrecord10.1088/1742-5468/2015/11/P11008en
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.typeJournal Article/Reviewen


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