Model study of the sign problem in the mean-field approximation

Details Model study of the sign problem in the mean-field approximation Model study of the sign problem in the mean-field approximation

2006-10-24

arxiv.org/abs/hep-ph/0610323v3

Phys.Rev.D75:036002,2007

Physics

High Energy Physics

High Energy Physics - Phenomenology

14 page, 18 figures, typos corrected, references added, some clarification in sec.II

Scientific paper

10.1103/PhysRevD.75.036002

We argue the sign problem of the fermion determinant at finite density. It is unavoidable not only in Monte-Carlo simulations on the lattice but in the mean-field approximation as well. A simple model deriving from Quantum Chromodynamics (QCD) in the double limit of large quark mass and large quark chemical potential exemplifies how the sign problem arises in the Polyakov loop dynamics at finite temperature and density. In the color SU(2) case our mean-field estimate is in excellent agreement with the lattice simulation. We combine the mean-field approximation with a simple phase reweighting technique to circumvent the complex action encountered in the color SU(3) case. We also investigate the mean-field free energy, from the saddle-point of which we can estimate the expectation value of the Polyakov loop.

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