Double Flip Move for Ising Models with Mixed Boundary Conditions

TL;DR

This paper introduces a double flip move to enhance the Swendsen-Wang algorithm for Ising models with mixed boundary conditions, improving mixing efficiency below the critical temperature.

Contribution

The paper proposes a novel double flip move combining geometric and spin flips, with proven detailed balance and demonstrated empirical efficiency.

Findings

Proven detailed balance of the double flip move.

Empirical evidence of improved mixing efficiency.

Applicable to symmetric and approximately symmetric models.

Abstract

This note introduces the double flip move for accelerating the Swendsen-Wang algorithm for Ising models with mixed boundary conditions below the critical temperature. The double flip move consists of a geometric flip of the spin lattice followed by a spin value flip. Both the symmetric and approximately symmetric models are considered. We prove the detailed balance of the double flip move and demonstrate its empirical efficiency in mixing.