Ising models on the hydrogen peroxide and other lattices

TL;DR

This study uses Monte Carlo simulations to analyze the critical behavior of the Ising model on various three-dimensional lattices, refining universal parameters and correction-to-scaling estimates with improved accuracy.

Contribution

It provides new, more precise estimates of critical exponents and correction parameters for the 3D Ising universality class across multiple lattice types.

Findings

Critical exponents agree with 3D Ising universality class.

Large correction-to-scaling amplitudes observed.

Refined universal parameters with reduced error margins.

Abstract

We perform a Monte Carlo analysis of the Ising model on many three-dimensional lattices. By means of finite-size scaling we obtain the critical points and determine the scaling dimensions. As expected, the critical exponents agree with the three-dimensional Ising universality class for all models. The irrelevant field, as revealed by the correction-to-scaling amplitudes, appears to be relatively large. Combining the Monte Carlo results for the hydrogen peroxide lattice with those for five other three-dimensional lattices, we obtain a set of data covering a wide range of the irrelevant temperature field. This is helpful in the determination of the parameters describing the corrections to scaling. As a consequence, new results are obtained for the universal parameters describing Ising criticality in three dimensions, with reduced error margins in comparison with earlier Monte Carlo analyses. The critical exponents describing the thermodynamic singularities are determined by the temperature renormalization exponent $y_t = 1.58693 (9)$ and the magnetic renormalization exponent $y_h = 2.48178 (5)$. The corrections to scaling are governed by the irrelevant exponent $y_1 = -0.821 (5)$.