Time-Dependent Order Parameters in Spin-Glasses

It is proposed that the spin-glass phase is described by two order parameters q (x) =〈{S₈ (0) S₈ (tₗ) 〉}₀ₕ and (x) =0^{tₗ} (t) dt, that measure the relaxations of the average autocorrelation and susceptibility along macroscopic time scales, tₗ, which are parametrized in a decreasing order by x0, 1. The function q decays from a finite value at t₁ to zero at t₀, while increases from (1) to a value (0) which is independent of temperature in the mean-field limit. The equilibrium results agree with Parisi's replica solution.