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

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.