Thermodynamics of free domain wall fermions

Abstract

Studying various thermodynamic quantities for the free domain wall fermions for both finite and infinite fifth dimensional extent N₅, we find that the lattice corrections are minimal for N_T≥10 for both energy density and susceptibility, for its irrelevant parameter M in the range 1.45-1.50. The correction terms are, however, quite large for small lattice sizes of N_T≤8. We propose modifications of the domain wall operator, as well as the overlap operator, to reduce the finite cutoff effects to within 10% of the continuum results of the thermodynamic quantities for the currently used N_T=6-8 lattices. Incorporating the chemical potential, we show that divergences proportional to μ²/a² are absent for a large class of such domain wall fermion actions although the chiral symmetry is broken for μ≠0 at any finite lattice spacing.