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.

28 pages

References in corpus (6)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Logarithmic Finite-Size Effects on Interfacial Free Energies: Phenomenological Theory and Monte Carlo Studies
• Thermodynamic Casimir Forces between a Sphere and a Plate: Monte Carlo Simulation of a Spin Model
• A Monte Carlo study of the three-dimensional XY universality class:Universal amplitude ratios
• Thermodynamic Casimir Effect in Films: the Exchange Cluster Algorithm
• Geometric Allocation Approaches in Markov Chain Monte Carlo

Cited by in corpus (6)

• Restoring isotropy in a three-dimensional lattice model: The Ising universality class
• Two- and three-point functions at criticality: Monte Carlo simulations of the improved three-dimensional Blume-Capel model
• Charting the scaling region of the Ising universality class in two and three dimensions
• ${\varphi }^4$ lattice model with cubic symmetry in three dimensions: RG-flow and first order phase transitions
• Cluster percolation in the three-dimensional $\pm J$ random-bond Ising model
• The interface tension in the improved Blume-Capel model