# The Marginal Stability of the Meta-stable Thouless-Anderson-Palmer States

## TL;DR

This paper extends the analysis of the complexity of meta-stable states in spin glasses by including higher moments, revealing marginal stability at certain temperatures and providing insights into the temperature dependence of the Gibbs potential.

## Contribution

It introduces the inclusion of the fourth moment of magnetizations in the complexity analysis, revealing marginal stability of states at low temperatures.

## Key findings

- Maximum complexity occurs at the boundary below a critical temperature.
- States exhibit marginal stability at low temperatures.
- Gibbs potential varies with temperature, indicating stability changes.

## Abstract

The existing investigations on the complexity are extended. In addition to the Edward-Anderson Parameter q_2 the fourth moment q_4 of the magnetizations m_i 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.