Approach to the thermodynamic limit in lattice QCD atμ≠0

2007/09/14 by K. Splittorff, J. J. M. Verbaarschot · 3 citations
Mathematics · Physics and Astronomy · #Algorithm #Combinatorics #Computation #Condensed matter physics #Finite volume method #High-Energy Particle Collisions Research #Lattice (music) #Lattice QCD #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Order (exchange) #Particle physics #Particle physics theoretical and experimental studies #Phase transition #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Thermodynamic limit #Thermodynamics #hep-lat

paper · pdf · doi:10.1103/physrevd.77.014514

published as Phys.Rev.D77:014514,2008 · 9 pages, 5 figures

arxiv created 2007/09/14 · openalex publication_date 2008/01/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The expectation value of the complex phase factor of the fermion determinant is computed to leading order in the p expansion of the chiral Lagrangian. The computation is valid for \ensuremathμ<m_\ensuremathπ/2 and determines the dependence of the sign problem on the volume and on the geometric shape of the volume. In the thermodynamic limit with L_i\ensuremath→\ensuremath∞ at fixed temperature 1/L₀, the average phase factor vanishes. In the low temperature limit where L_i/L₀ is fixed as L_i becomes large, the average phase factor approaches 1 for \ensuremathμ<m_\ensuremathπ/2. The results for a finite volume compare well with lattice results obtained by Allton et al. After taking appropriate limits, we reproduce previously derived results for the ϵ regime and for one-dimensional QCD. The distribution of the phase itself is also computed.

Citations

• Remarks on the multiparameter reweighting method for the study of lattice QCD at nonzero temperature and density
• QCD sign problem for small chemical potential
• Critical point of QCD at finite T and , lattice results for physical quark masses
• Pressure and nonlinear susceptibilities in QCD at finite chemical potentials
• Imaginary chemical potentials and the phase of the fermionic determinant
• Sign problem via imaginary chemical potential
• The solution of a chiral random matrix model with complex eigenvalues

Cited by

• The density in the density of states method
• LESSONS FROM RANDOM MATRIX THEORY FOR QCD AT FINITE DENSITY
• Phase diagram of dynamical twisted-mass Wilson fermions at finite isospin chemical potential

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• Lattice QCD at High Temperature and Density