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

© 2009 The American Physical Society. We acknowledge partial financial support from Ministerio de Ciencia e Innovación Spain through research Contract No. FIS2006-08533.
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 twodimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4.
Ministerio de Ciencia e Innovación, Spain
Depto. de Física Teórica
Fac. de Ciencias Físicas
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