Spherical Spin-Glass-Coulomb-Gas Duality: Solution beyond Mean-Field Theory

We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions and a global spherical constraint at zero magnetic field. The replicated spin-glass Hamiltonian is mapped onto a Coulomb gas of logarithmically interacting particles confined by a logarithmic single particle potential. The precise free energy is obtained by analyzing the Painleve tau(IV)[n] function in the n -> 0 limit. The large-N thermodynamics exactly recovers that of Kosterlitz, Thouless, and Jones [Phys. Rev. Lett. 36, 1217 (1976)]. It is hoped that the approach here can be extended to apply to systems beyond the spherical model, particularly those in which destabilizing terms lead to replica symmetry breaking.