A_+/A_-, alpha, nu, and f_s xi^3 from 3D Ising Energy and Specific Heat

TL;DR

This paper analyzes Monte Carlo data for the 3D Ising model's energy and specific heat near criticality, providing precise estimates of critical exponents, amplitude ratios, and universal combinations through finite size scaling.

Contribution

It offers new, highly accurate estimates of critical exponents, amplitude ratios, and universal quantities for the 3D Ising model using finite size scaling analysis.

Findings

Estimated critical exponent nu = 0.6308(10).

Determined amplitude ratio A_+/A_- ≈ 0.56.

Calculated universal combination f_s xi^3.

Abstract

We analyse Monte Carlo data for the energy and specific heat at and close to the critical point of the 3D cubic Ising model. From the finite size scaling of the energy E and the specific heat C at criticality we obtain the estimate nu = 0.6308(10). Furthermore, one obtains precise estimates for the ``backgrounds'' (nonsingular parts) E_ns and C_ns. Fitting solely off critical energy estimates to a scaling law, we find depending on the choice of the reduced temperature, either A_+/A_- = 0.550(12) and alpha=0.1115(37), or A_+/A_- = 0.567(16) and alpha=0.1047(48). Including information from the data at T_c, we obtain the estimate A_+/A_- = 0.560(10). We also determine the universal combination f_s xi^3 in both phases.