Thermodynamics of the ideal overlap quarks on the lattice

The thermodynamics of massless ideal gas of overlap quarks has been investigated both analytically and numerically for both zero and nonzero baryon chemical potential. Any {mu}{sup 2} divergence is shown analytically to be absent for a class of actions with nonzero chemical potential. All such actions are shown to violate chiral invariance. While the parameter M can be shown to be irrelevant in the continuum limit, as expected, it is shown numerically that the continuum limit can be reached with relatively coarser lattices for 1.5{<=}M{<=}1.6. Numerical limitations of the existing method of introduction of chemical potential are demonstrated. Finally we also show that the energy density for the massive overlap fermions has the correct continuum limit.