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

Understand

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.