The marginal stability of the metastable TAP states

Abstract

Abstract The existing investigations on the complexity are extended. In addition to the Edward–Anderson parameter q 2 the fourth moment q 4 = 1 / N ∑ i m i 4 of the magnetizations m i is included to the set of constrained variables and the constrained complexity Σ(T; q 2, q 4) is numerical determined. The maximum of Σ(T; q 2, q 4) (representing the total complexity) sticks at the boundary for temperatures at and below a new critical temperature. This implies marginal stability for the nearly all metastable states. The temperature dependence of the lowest value of the Gibbs potential consistent with various physical requirements is presented.