Commun. Comput. Phys., 14 (2013), pp. 355-369.


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

J. Kaupuzs 1*, R. V. N. Melnik 2, J. Rimsans 1

1 Institute of Mathematics and Computer Science, University of Latvia, 29 Raina Boulevard, LV1459, Riga, Latvia; and Institute of Mathematical Sciences and Information Technologies, University of Liepaja, 14 Liela Street, Liepaja LV-3401, Latvia.
2 Wilfrid Laurier University, Waterloo, Ontario, Canada, N2L 3C5.

Received 24 May 2012; Accepted (in revised version) 12 September 2012
Available online 12 December 2012
doi:10.4208/cicp.240512.120912a

Abstract

The singularity of specific heat C_V of the three-dimensional Ising model is studied based on Monte Carlo data for lattice sizes $L \le 1536$. Fits of two data sets, one corresponding to certain value of the Binder cumulant and the other - to the maximum of C_V, provide consistent values of C_0 in the ansatz $C_V(L) = C_0 + A L^{\alpha/\nu}$ at large L, if $\alpha/\nu=0.196(6)$. However, a direct estimation from our $C_V^{max}$ data suggests that $\alpha/\nu$, most probably, has a smaller value (e.g., $\alpha/\nu=0.113(30)$). 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.

AMS subject classifications: 65C05, 82B20, 82B80, 82B27

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Key words: Ising model, Monte Carlo simulation, specific heat, finite-size scaling, critical exponents.

*Corresponding author.
Email: kaupuzs@latnet.lv (J. Kaupuzs), rmelnik@wlu.ca (R. V. N. Melnik), rimshans@mii.lu.lv (J. Rimsans)
 

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