Chiral symmetry restoration in anisotropicQED3

Abstract

We present results from a Monte Carlo simulation of noncompact lattice QED in three dimensions in which an explicit anisotropy $\ensuremath{\kappa}$ between $x$ and $y$ hopping terms has been introduced into the action. Using a parameter set corresponding to broken chiral symmetry in the isotropic limit $\ensuremath{\kappa}=1$, we study the chiral condensate on ${16}^{3}$, ${20}^{3}$, and ${24}^{3}$ lattices as $\ensuremath{\kappa}$ is varied, and fit the data to an equation of state which incorporates anisotropic volume corrections. The value ${\ensuremath{\kappa}}_{c}$ at which chiral symmetry is apparently restored is strongly volume dependent, suggesting that the transition may be a crossover rather than a true phase transition. In addition we present results on ${16}^{3}$ lattices for the scalar meson propagator, and for the Landau gauge-fixed fermion propagator. The scalar mass approaches the pion mass at large $\ensuremath{\kappa}$, consistent with chiral symmetry restoration, but the fermion remains massive at all values of $\ensuremath{\kappa}$ studied, suggesting that strong infrared fluctuations persist into the chirally symmetric regime. Implications for models of high-${T}_{c}$ superconductivity based on anisotropic ${\mathrm{QED}}_{3}$ are discussed.