The state space of short-range Ising spin glasses: the density of states

TL;DR

This paper investigates the structure of the state space in finite Ising spin glass models by analyzing global and local density of states, comparing different interaction distributions, and discussing implications for state space complexity.

Contribution

It introduces new measures for local state density and explores whether the local density of states grows exponentially, providing insights into the structure of spin glass state spaces.

Findings

Comparison of uniform and Gaussian interaction distributions.

Discussion on exponential growth of local density of states.

Implications for the structure of the spin glass state space.

Abstract

The state space of finite square and cubic Ising spin glass models is analysed in terms of the global and the local density of states. Systems with uniform and gaussian probability distribution of interactions are compared. Different measures for the local state density are presented and discussed. In particular the question whether the local density of states grows exponentially or not is considered. The direct comparison of global and local densities leads to consequences for the structure of the state space.