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 Painlevé τ{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)10.1103/PhysRevLett.36.1217]. 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.
Akhanjee
Shimul
S
Condensed Matter Theory Laboratory, RIKEN, Wako, Saitama, 351-0198, Japan. shimul@riken.jp
Rudnick
Joseph
J