Non-Commutativity of the Zero Chemical Potential Limit and the Thermodynamic Limit in Finite Density Systems

Abstract

Monte Carlo simulations of finite density systems are often plagued by the complex action problem. We point out that there exists certain non-commutativity in the zero chemical potential limit and the thermodynamic limit when one tries to study such systems by reweighting techniques. This is demonstrated by explicit calculations in a Random Matrix Theory, which is thought to be a simple qualitative model for finite density QCD. The factorization method allows us to understand how the non-commutativity, which appears at the intermediate steps, cancels in the end results for physical observables.

arXiv comment7 pages, 9 figures

References in corpus (17)

• The QCD phase diagram for small densities from imaginary chemical potential
• Lattice determination of the critical point of QCD at finite T and μ
• On the Phase Diagram of QCD
• The QCD thermal phase transition in the presence of a small chemical potential
• Finite density QCD via imaginary chemical potential
• A new method to study lattice QCD at finite temperature and chemical potential
• Random Matrix Theory and Chiral Symmetry in QCD
• Random matrix model of QCD at finite density and the nature of the quenched limit
• Lattice QCD at Finite Density -- An introductory review
• Almost-Hermitian Random Matrices: Eigenvalue Density in the Complex Plane
• A new approach to the complex-action problem and its application to a nonperturbative study of superstring theory
• Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
• The factorization method for systems with a complex action -a test in Random Matrix Theory for finite density QCD-
• New proposal for numerical simulations of theta-vacuum like systems
• Fermion determinants in matrix models of QCD at nonzero chemical potential
• Remarks on the multi-parameter reweighting method for the study of lattice QCD at non-zero temperature and density
• Random Matrices and the Convergence of Partition Function Zeros in Finite Density QCD

Cited by in corpus (9)

• The density of states method at non-zero chemical potential
• Dense Quarks, and the Fermion Sign Problem, in a SU(N) Matrix Model
• Random matrix analysis of the QCD sign problem for general topology
• Progress in the numerical studies of the type IIB matrix model
• A general approach to the sign problem - the factorization method with multiple observables
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Applying constrained simulations for low temperature lattice QCD at finite baryon chemical potential
• The sign problem across the QCD phase transition
• Dynamical Compactification of Extra Dimensions in the Euclidean IKKT Matrix Model via Spontaneous Symmetry Breaking