Towards QCD thermodynamics using exact chiral symmetry on lattice

The thermodynamics of massless ideal gas of overlap quarks has been investigated numerically for both zero and nonzero baryon chemical potential $\mu$. While the parameter M has been shown to be irrelevant in the continuum limit, it is shown numerically that the continuum limit can be reached with relatively coarser lattices for certain range of M. Numerical limitation of the existing method of introduction of chemical potential in the overlap formalism is discussed. We have also studied the energy density of free domain wall fermions in the absence of $\mu$ and estimated the extent of lattice in the fifth dimension $L_5$ for which the overlap results are recovered. Interestingly, this value of $L_5$ is also minimum for the same range of M found in the overlap case.