A variance reduced estimator of the connected two-point function in the presence of a broken Z_2 symmetry

TL;DR

This paper introduces a variance reduced estimator for the connected two-point function in models with broken Z_2 symmetry, enabling high-precision correlation length measurements and universal ratio estimates.

Contribution

It presents a novel variance reduction technique using the exchange or geometric cluster algorithm for the connected two-point function in Z_2-symmetric models.

Findings

Significant variance reduction achieved in simulations.

High-precision correlation length measurements.

Estimates of universal amplitude ratios for the 3D Ising universality class.

Abstract

The exchange or geometric cluster algorithm allows us to define a variance reduced estimator of the connected two-point function in the presence of a broken Z_2-symmetry. We present first numerical tests for the improved Blume-Capel model on the simple cubic lattice. We perform simulations for the critical isotherm, the low temperature phase at vanishing external field and, for comparison, also the high temperature phase. For the connected two-point function a substantial reduction of the variance can be obtained, allowing us to compute the correlation length with high precision. Based on these results, estimates for various universal amplitude ratios that characterise the universality class of the three-dimensional Ising model are computed.