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Scaling Regimes and the Singularity of Specific Heat in the 3D Ising Model

Published online by Cambridge University Press:  03 June 2015

J. Kaupužs ,
R. V. N. Melnik  and
J. Rimšāns
J. Kaupužs*
Affiliation:
Institute of Mathematics and Computer Science, University of Latvia, 29 Raiņa Boulevard, LV1459, Riga, Latvia Institute of Mathematical Sciences and Information Technologies, University of Liepaja, 14 Liela Street, Liepaja LV-3401, Latvia
R. V. N. Melnik*
Affiliation:
Wilfrid Laurier University, Waterloo, Ontario, Canada, N2L 3C5
J. Rimšāns*
Affiliation:
Institute of Mathematics and Computer Science, University of Latvia, 29 Raiņa Boulevard, LV1459, Riga, Latvia Institute of Mathematical Sciences and Information Technologies, University of Liepaja, 14 Liela Street, Liepaja LV-3401, Latvia
*
Corresponding author.Email:kaupuzs@latnet.lv
Email:rmelnik@wlu.ca
Email:rimshans@mii.lu.lv
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Abstract

The singularity of specific heat CV of the three-dimensional Ising model is studied based on Monte Carlo data for lattice sizes L≤1536. Fits of two data sets, one corresponding to certain value of the Binder cumulant and the other — to the maximum of CV, provide consistent values of C0 in the ansatz CV(L)=C0+ALα/ν at large L, if α/ν=0.196(6). However, a direct estimation from our data suggests that α/ν, most probably, has a smaller value (e.g., α/ν= 0.113(30)). Thus, the conventional power-law scaling ansatz can be questioned because of this inconsistency. We have found that the data are well described by certain logarithmic ansatz.

Keywords

65C0582B2082B8082B27Ising modelMonte Carlo simulationspecific heatfinite-size scalingcritical exponents
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 2 , August 2013 , pp. 355 - 369
Copyright
Copyright © Global Science Press Limited 2013

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