Staggered-magnetization approach to spin-glasses

Abstract

A method is developed to solve the Sherrington-Kirkpatrick infinite-ranged spin-glass model, considering the staggered magnetizations associated with the eigenvalue spectrum of the random interaction matrix as the spin-glass order parameters. It is shown that the spin-glass ordering is not associated with a macroscopic condensation of eigenstates, but instead each of the $N$ eigenstates acquires, below $T_c$, nonzero magnetization of $O\mathrm{}\left(1\right)\mathrm{}$.