The Marginal Stability of the Meta-stable Thouless-Anderson-Palmer States
Abstract
The existing investigations on the complexity are extended. In addition to the Edward-Anderson Parameter q2 the fourth moment q4 of the magnetizations mi is included to the set of constrained variables and the constrained complexity is numerically determined. The maximum of the constrained complexity (representing the total complexity) sticks at the boundary for temperatures at and below a new critical temperature. This implies marginal stability. The temperature dependence of lowest value of the Gibbs potential consistent with all requirements is presented.
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