Mean-value identities as an opportunity for Monte Carlo error reduction

Abstract

In the Monte Carlo simulation of both Lattice field-theories and of models of Statistical Mechanics, identities verified by exact mean-values such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well known and sensitive tests of thermalization bias as well as checks of pseudo random number generators. We point out that they can be further exploited as "control variates" to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the two dimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4.

10 pages, 2 tables. References updated and typos corrected

References in corpus (11)

• Locality and exponential error reduction in numerical lattice gauge theory
• Critical exponents of the three dimensional diluted Ising model
• Monte Carlo Simulations of Spin Glasses at Low Temperatures
• Finite size effects on measures of critical exponents in d=3 O(N) models
• Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus
• On the Phase Structure of the 3D Edwards Anderson Spin Glass
• Nonequilibrium spin glass dynamics from picoseconds to 0.1 seconds
• About the overlap distribution in mean field spin glass models
• Cross-correlations in scaling analyses of phase transitions
• Tethered Monte Carlo: computing the effective potential without critical slowing down
• A new test for random number generators: Schwinger-Dyson equations for the Ising model

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• Equation Planting: A Tool for Benchmarking Ising Machines
• Tethered Monte Carlo: Managing rugged free-energy landscapes with a Helmholtz-potential formalism
• Numerical test of the Cardy-Jacobsen conjecture in the site-diluted Potts model in three dimensions
• Percolation of Fortuin-Kasteleyn clusters for the random-bond Ising model
• Evidence of many thermodynamic states of the three-dimensional Ising spin glass
• Finite-Size Scaling at fixed Renormalization-Group invariant
• Improvement of Monte Carlo estimates with covariance-optimized finite-size scaling at fixed phenomenological coupling
• Deepening the knowledge of Spin Glasses: Metastate, Off-equilibrium phenomena and Temperature Chaos