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Volume 14, Issue 2
Scaling Regimes and the Singularity of Specific Heat in the 3D Ising Model

J. Kaupužs, R. V. N. Melnik & J. Rimšāns

DOI: 10.4208/cicp.240512.120912a

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

Published online: 2014-08

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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 $C^{max}_V$ 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.

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@Article{CiCP-14-355, author = {J. Kaupužs, R. V. N. Melnik and J. Rimšāns}, title = {Scaling Regimes and the Singularity of Specific Heat in the 3D Ising Model}, journal = {Communications in Computational Physics}, year = {2014}, volume = {14}, number = {2}, pages = {355--369}, 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 $C^{max}_V$ 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.240512.120912a}, url = {http://global-sci.org/intro/article_detail/cicp/7163.html} }
TY - JOUR T1 - Scaling Regimes and the Singularity of Specific Heat in the 3D Ising Model AU - J. Kaupužs, R. V. N. Melnik & J. Rimšāns JO - Communications in Computational Physics VL - 2 SP - 355 EP - 369 PY - 2014 DA - 2014/08 SN - 14 DO - http://doi.org/10.4208/cicp.240512.120912a UR - https://global-sci.org/intro/article_detail/cicp/7163.html KW - AB -

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 $C^{max}_V$ 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.

J. Kaupužs, R. V. N. Melnik and J. Rimšāns. (2014). Scaling Regimes and the Singularity of Specific Heat in the 3D Ising Model. Communications in Computational Physics. 14 (2). 355-369. doi:10.4208/cicp.240512.120912a
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