Systematic enumeration of configuration classes for entropic sampling of Ising models

TL;DR

This paper introduces a systematic method for enumerating configuration classes in the Ising model, enabling precise sampling, interpolation, and analysis of thermodynamic properties and phase transitions.

Contribution

It presents a novel systematic enumeration technique for configuration classes in the Ising model, improving sampling accuracy and enabling detailed finite-size scaling analysis.

Findings

Accurate enumeration of configuration classes for L=10 to 30.

Reliable estimation of microcanonical averages and configuration counts.

Determination of the critical line in the h-T plane.

Abstract

We describe a systematic method for complete enumeration of configuration classes (CCs) of the spin-1/2 Ising model in the energy-magnetization plane. This technique is applied to the antiferromagnetic Ising model in an external magnetic field on the square lattice, which is simulated using the tomographic entropic sampling algorithm. We estimate the number of configurations, $\Omega(E,m,L)$, and related microcanonical averages, for all allowed energies $E$ and magnetizations $m$ for $L = 10$ to 30, with $\Delta L = 2$. With prior knowledge of the CCs, we can be sure that all allowed classes are sampled during the simulation. Complete enumeration of CCs also enables us to use the final estimate of $\Omega(E,m,L)$ to obtain good initial estimates, $\Omega_0(E,m,L')$, for successive system sizes ($L' > L$) through a two-dimensional interpolation. Using these results we calculate canonical averages of the thermodynamic quantities of interest as continuous functions of temperature $T$ and external field $h$. In addition, we determine the critical line in the $h$-$T$ plane using finite-size scaling analysis, and compare these results with several approximate theoretical expressions.