Overlap Fermions on a $20^{4}$ Lattice

We report results on hadron masses, fitting of the quenched chiral log, and quark masses from Neuberger's overlap fermion on a quenched $20^4$ lattice with lattice spacing $a = 0.15$ fm. We used the improved gauge action which is shown to lower the density of small eigenvalues for $H^2$ as compared to the Wilson gauge action. This makes the calculation feasible on 64 nodes of CRAY-T3E. Also presented is the pion mass on a small volume ($6^3 \times 12$ with a Wilson gauge action at $\beta = 5.7$). We find that for configurations that the topological charge $Q \ne 0$, the pion mass tends to a constant and for configurations with trivial topology, it approaches zero possibly linearly with the quark mass