# Self-organized critical behavior and marginality in Ising spin glasses

## TL;DR

This study numerically investigates the critical and marginal behavior of one-dimensional long-range Ising spin glasses after a quench, revealing self-organized criticality and divergence in susceptibility for certain interaction ranges.

## Contribution

It demonstrates the emergence of self-organized criticality and marginal stability in long-range Ising spin glasses for specific interaction decay exponents, extending understanding of spin glass dynamics.

## Key findings

- Susceptibility diverges logarithmically for σ ≤ 1/2.
- States exhibit marginal stability when σ ≤ 1/2.
- System behavior transitions at σ = 1/2, indicating different regimes.

## Abstract

We have studied numerically the states reached in a quench from various temperatures in the one-dimensional fully-connected Kotliar, Anderson and Stein Ising spin glass model. This is a model where there are long-range interactions between the spins which falls off a\ s a power $\sigma$ of their separation. We have made a detailed study in particular of the energies of the states reached in a quench from infinite temperature and their overlaps, including the spin glass susceptibility. In the regime where $\sigma \le 1/2$, where th\ e model is similar to the Sherrington-Kirkpatrick model, we find that the spin glass susceptibility diverges logarithmically with increasing $N$, the number of spins in the system, whereas for $\sigma> 1/2$ it remains finite. We attribute the behavior for $\sigma \le 1/\ 2$ to \emph {self-organized critical behavior}, where the system after the quench is close to the transition between states which have trivial overlaps and those with the non-trivial overlaps associated with replica symmetry breaking. We have also found by studying the d\ istribution of local fields that the states reached in the quench have marginal stability but only when $\sigma \le 1/2$.