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arXiv · 1110.5749

Complex Langevin dynamics: criteria for correctness

Gert Aarts·Frank A. James·Erhard Seiler·Ion-Olimpiu Stamatescu
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Abstract

The complex Langevin method is a leading candidate for solving the sign problem occurring in various physical situations, notably QCD at finite chemical potential. Its most vexing problem is `convergence to the wrong limit', where the simulation gives a well defined, but incorrect, result. Here, we first outline a formal justification of the method and identify points at which it might fail. From these we derive a condition that must be satisfied in order for correct results to be obtained. We then apply these ideas to the three-imensional SU(3) spin model at finite chemical potential and show strong indications that complex Langevin dynamics yields correct results in this theory.

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Gert Aarts, Frank A. James, Erhard Seiler, Ion-Olimpiu Stamatescu. 2011-10-26. Complex Langevin dynamics: criteria for correctness. https://arxiv.org/abs/1110.5749

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