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

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

2009-04-22

arxiv.org/abs/0904.3415v2

Phys. Rev. E 79, 051109 (2009)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 2 tables. References updated and typos corrected

Scientific paper

10.1103/PhysRevE.79.051109

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.

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