Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1999-08-17
Phys.Rev.D61:076005,2000
Physics
High Energy Physics
High Energy Physics - Lattice
17 pages, 14 figures, typos corrected
Scientific paper
10.1103/PhysRevD.61.076005
We apply the Glasgow method for lattice QCD at finite chemical potential to a schematic random matrix model (RMM). In this method the zeros of the partition function are obtained by averaging the coefficients of its expansion in powers of the chemical potential. In this paper we investigate the phase structure by means of Glasgow averaging and demonstrate that the method converges to the correct analytically known result. We conclude that the statistics needed for complete convergence grows exponentially with the size of the system, in our case, the dimension of the Dirac matrix. The use of an unquenched ensemble at $\mu=0$ does not give an improvement over a quenched ensemble. We elucidate the phenomenon of a faster convergence of certain zeros of the partition function. The imprecision affecting the coefficients of the polynomial in the chemical potential can be interpeted as the appearance of a spurious phase. This phase dominates in the regions where the exact partition function is exponentially small, introducing additional phase boundaries, and hiding part of the true ones. The zeros along the surviving parts of the true boundaries remain unaffected.
Halasz Miklos-Adam
Osborn James C.
Stephanov Mikhail A.
Verbaarschot Jacobus J. M.
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