Study of the ultrametric structure of Finite Dimensional Spin Glasses throught a constrained Monte Carlo dynamics

TL;DR

This paper investigates the ultrametric structure of finite-dimensional spin glasses using a constrained Monte Carlo method, revealing that in the thermodynamic limit, their low-energy states exhibit ultrametricity similar to the SK model.

Contribution

It demonstrates that finite-dimensional 4D EA spin glasses exhibit ultrametric low-energy state structures, extending the understanding from mean-field models.

Findings

Ultrametric structure confirmed in 4D EA spin glasses.

Constrained Monte Carlo effectively explores low-energy states.

Results align with properties of the SK model in the thermodynamic limit.

Abstract

We report a very detailed relation about the study, by a constrained Monte Carlo dynamic, of a 4D EA spin glass model (J=+/- 1). In particular we concentrate our attention on the behaviour of the system under different bounds imposed in order to optimize the dynamic and try to understand the low energy states structure. We find that in the thermodynamic limit this structure is clearly ultrametric as already established for the SK model.