Dynamical properties of the hypercell spin glass model

TL;DR

This paper investigates how the dimensionality affects the dynamical behavior of spin glasses using damage spreading techniques in Monte Carlo simulations of hypercubic models.

Contribution

It introduces a comparative study of 2D hypercubic cells and higher-dimensional lattices to understand their dynamical properties and convergence to mean field behavior.

Findings

Damage spreading varies with dimension

Finite-dimensional models resemble mean field in high dimensions

Dimensionality influences sensitivity to initial conditions

Abstract

The spreading of damage technique is used to study the sensibility to initial conditions in a heath bath Monte Carlo simulation of the spin glass hypercubic cell model. Since the hypercubic cell in dimension 2D and the hypercubic lattice in dimension D resemble each other closely at finite dimensions and both converge to mean field when dimension goes to infinity, it allows us to study the effect of dimensionality on the dynamical behavior of spin glasses.