Precise Phase Structure in Four-fermion Interaction Model on Torus

Abstract

We investigate finite-size effects on chiral symmetry breaking in a four-fermion interaction model at a finite temperature and a chemical potential. Applying the imaginary time formalism, the thermal quantum field theory is constructed on an $S^1$ in the imaginary time direction. In this paper, the finite-size effect is introduced by a compact $S^1$ spatial direction with a $\mathrm{U}(1)$-valued boundary condition. Thus, we study the model on a ${\mathbb{R}}^{D-2}\times S^1\times S^1$ torus. Phase diagrams are obtained by evaluating the local minima of the effective potential in the leading order of the $1/N$ expansion. From the grand potential, we calculate the particle number density and the pressure, then we illustrate the correspondence with the phase structure. We obtain a stable size for which the sign of the pressure flips from negative to positive as the size decreases. Furthermore, the finite chemical potential expands the parameter range that the stable size exists.

arXiv comment18 pages, 16 figures

References in corpus (21)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Dynamical symmetry breaking in curved spacetime -review-
• Phase Structure of Four-Fermion Theories at Finite Temperature and Chemical Potential in Arbitrary Dimensions
• Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Sign Flip in the Casimir Force for Interacting Fermion Systems
• Strongly Interacting Fermions and Phases of the Casimir Effect
• Interacting Fermions, Boundaries, and Finite Size Effects
• Cooper pairing and finite-size effects in a NJL-type four-fermion model
• Casimir effect for nucleon parity doublets
• Lattice-fermionic Casimir effect and topological insulators
• Casimir effect for lattice fermions
• Finite-size effects on the Phase Structure of the Walecka Model
• Dynamical Symmetry Breaking on a Cylinder in Magnetic Field
• Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields: Phase diagram and the first-order phase transitions
• Dual Fermion Condensates in Curved Space
• Nonperturbative Casimir Effects in Field Theories: aspects of confinement, dynamical mass generation and chiral symmetry breaking
• Deconfinement transition and Black Holes
• $D$ mesons as a probe of Casimir effect for chiral symmetry breaking
• Four-Fermion Interaction Model on ${\mathcal{M}}^{D-1}\otimes S^1$
• Statistical Mechanics of Relativistic Aynon-like Systems

Cited by in corpus (1)

• Effective model for pure Yang-Mills theory on ${\mathbb{T}}^2\times {\mathbb{R}}^2$ with Polyakov loops