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

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

Published online: 2014-08

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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 = {}, 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 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 & J. Rimšāns. (2020). 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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