Spin-glass model with partially annealed asymmetric bonds

Abstract

We have considered the two-spin interaction spherical spin-glass model with asymmetric bonds (coupling constants). Besides the usual interactions between spins and bonds and between the spins and a thermostat with temperature ${T}_{\ensuremath{\sigma}}$ there is also an additional factor: the bonds are not assumed random a priori but interact with some other thermostat at the temperature ${T}_{J}.$ We show that when the bonds are frozen with respect to the spins a first order phase transition to a spin-glass phase occurs, and the temperature of this transition tends to zero if ${T}_{J}$ is large. Our analytical results show that a spin-glass phase can exist in mean-field models with nonrelaxational dynamics.