Finite dimensional corrections to mean field in a short-range p-spin glassy model

TL;DR

This paper investigates finite-dimensional effects in a short-range p-spin glass model, revealing discrepancies between perturbative predictions and simulations due to non-perturbative local freezing phenomena.

Contribution

It introduces a short-range p-spin model with a tunable parameter for crossover to mean field behavior and identifies non-perturbative effects affecting system freezing.

Findings

Discrepancy between perturbative approach and simulations.

Finite probability of local less-frustrated regions.

Non-perturbative effects influence freezing temperature.

Abstract

In this work we discuss a short range version of the $p$-spin model. The model is provided with a parameter that allows to control the crossover with the mean field behaviour. We detect a discrepancy between the perturbative approach and numerical simulation. We attribute it to non-perturbative effects due to the finite probability that each particular realization of the disorder allows for the formation of regions where the system is less frustrated and locally freezes at a higher temperature.