Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice

Grzegorz Siudem , Agata Fronczak , Piotr Fronczak

Abstract

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic-to-paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models. © The Author(s) 2016.
Author Grzegorz Siudem ZFUZ
Grzegorz Siudem,,
- Physics of Complex Systems Divison
, Agata Fronczak ZFUZ
Agata Fronczak,,
- Physics of Complex Systems Divison
, Piotr Fronczak ZFUZ
Piotr Fronczak,,
- Physics of Complex Systems Divison
Journal seriesScientific Reports, ISSN 2045-2322
Issue year2016
Vol6
Pages33523-33523
Publication size in sheets0.3
Keywords in Englishlow temperature; model; partition coefficient; phase transition
DOIDOI:10.1038/srep33523
URL https://www.scopus.com/inward/record.uri?eid=2-s2.0-84990949398&partnerID=40&md5=eb0e245fe2eab09a7d3079d9f34633c8
Languageen angielski
Score (nominal)40
ScoreMinisterial score [Punktacja MNiSW] = 40.0, 28-11-2017, ArticleFromJournal
Ministerial score (2013-2016) [Punktacja MNiSW (2013-2016)] = 40.0, 28-11-2017, ArticleFromJournal
Publication indicators WoS Impact Factor [Impact Factor WoS]: 2016 = 4.259 (2) - 2016=4.847 (5)
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