Mean field theory of effective spin models as a baryon fugacity expansion

Abstract

The free energy of effective spin or "Polyakov line" models with a chemical potential, based on the U(N) group, does not depend on the chemical potential. In a mean field-inspired expansion, we show how the condition of unit determinant, taking U(N) to SU(N), reintroduces the chemical potential, and allows us to express the free energy, as a function of mean field variational parameters, in terms of an expansion in the baryon (rather than the quark) fugacity at each lattice site. We solve the SU(3) mean field equations numerically to determine the phase diagram and compute observables. We also calculate the first corrections to the leading order mean field results, and find that these can significantly shift the endpoint of a line of first order transitions. The problem of deriving an effective spin model from full QCD is discussed.

18 pages, 6 figures

References in corpus (4)

• Flux representation of an effective Polyakov loop model for QCD thermodynamics
• Monte Carlo simulation of the SU(3) spin model with chemical potential in a flux representation
• Testing Proposals for the Yang-Mills Vacuum Wavefunctional by Measurement of the Vacuum
• Inverse Monte-Carlo determination of effective lattice models for SU(3) Yang-Mills theory at finite temperature

Cited by in corpus (16)

• Controlling complex Langevin dynamics at finite density
• Complex Langevin dynamics and other approaches at finite chemical potential
• Comparison of complex Langevin and mean field methods applied to effective Polyakov line models
• Effective Polyakov line action from the relative weights method
• Finding the effective Polyakov line action for SU(3) gauge theories at finite chemical potential
• The potential of the effective Polyakov line action from the underlying lattice gauge theory
• Effective Polyakov line action from strong lattice couplings to the deconfinement transition
• Relative weights approach to SU(3) gauge theories with dynamical fermions at finite density
• Dual simulation of a Polyakov loop model at finite baryon density: phase diagram and local observables
• Large N lattice QCD and its extended strong-weak connection to the hypersphere
• Flux simulation of the SU(3) spin model at finite chemical potential
• A finite-density transition line for QCD with 695 MeV dynamical fermions
• Polyakov line actions from SU(3) lattice gauge theory with dynamical fermions via relative weights
• $\xi /{\xi }_{2nd}$ ratio as a tool to refine Effective Polyakov Loop models
• Non-Local effective SU(2) Polyakov-loop models from inverse Monte-Carlo methods
• Effective lattice Polyakov loop theory for finite temperature Yang-Mills