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

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≤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 C₀ in the ansatz C_V (L) =C₀+AL^α/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.