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We present results from a simulation of quenched overlap fermions withL\"uscher-Weisz gauge field action on lattices up to $24^3 48$ and for pionmasses down to $\approx 250$ MeV. Among the quantities we study are the pion,rho and nucleon masses, the light and strange quark masses, and the pion decayconstant. The renormalization of the scalar and axial vector currents is donenonperturbatively in the $RI-MOM$ scheme. The simulations are performed at twodifferent lattice spacings, $a \approx 0.1$ fm and $\approx 0.15$ fm, and ontwo different physical volumes, to test the scaling properties of our actionand to study finite volume effects. We compare our results with the predictionsof chiral perturbation theory and compute several of its low-energy constants.The pion mass is computed in sectors of fixed topology as well.Comment: 32 pages, 17 figure

Hadron spectrum, quark masses, and decay constants from light overlap fermions on large lattices