A hierarchy of self-consistent stochastic boundary conditions for Ising lattice simulations

TL;DR

This paper introduces a hierarchy of stochastic boundary conditions for Ising lattice simulations that effectively reduce finite size effects, improving accuracy in measuring thermodynamic properties and correlations.

Contribution

It presents a systematic hierarchy of SBCs that outperform traditional boundary conditions in Ising lattice Monte Carlo simulations.

Findings

SBCs of the two lowest orders compare favorably with PBC and analytical results.

Versatile SBCs accurately simulate different boundary types, including magnetized and open boundaries.

Measured properties include specific heat, magnetic susceptibility, and spin-spin correlations.

Abstract

We describe a hierarchy of stochastic boundary conditions (SBCs) that can be used to systematically eliminate finite size effects in Monte Carlo simulations of Ising lattices. For an Ising model on a $100 \times 100$ square lattice, we measured the specific heat, the magnetic susceptibility, and the spin-spin correlation using SBCs of the two lowest orders, to show that they compare favourably against periodic boundary conditions (PBC) simulations and analytical results. To demonstrate how versatile the SBCs are, we then simulated an Ising lattice with a magnetized boundary, and another with an open boundary, measuring the magnetization, magnetic susceptibility, and longitudinal and transverse spin-spin correlations as a function of distance from the boundary.