Numerical studies of a one-dimensional 3-spin spin-glass model with long-range interactions

TL;DR

This study investigates whether the finite-temperature glass transition observed in mean-field p-spin models persists in non-mean-field regimes by using a 3-spin model with tunable long-range interactions, revealing a loss of transition deep in the non-mean-field regime.

Contribution

It provides the first systematic numerical analysis of a 3-spin model with long-range interactions across different effective dimensions, connecting mean-field and non-mean-field behaviors.

Findings

Finite-temperature transition is absent deep in the non-mean-field regime.

Transition persists in the mean-field regime, consistent with theoretical predictions.

An apparent transition appears in the non-mean-field region, possibly due to finite-size effects.

Abstract

We study a p-spin spin-glass model to understand if the finite-temperature glass transition found in the mean-field regime of p-spin models, and used to model the behavior of structural glasses, persists in the non-mean-field regime. By using a 3-spin spin-glass model with long-range power-law diluted interactions we are able to continuously tune the (effective) space dimension via the exponent of the interactions. Monte Carlo simulations of the spin-glass susceptibility and the two-point finite-size correlation length show that deep in the non-mean-field regime the finite-temperature transition is lost, whereas this is not the case in the mean-field regime, in agreement with the prediction of Moore and Drossel [Phys. Rev. Lett. 89, 217202 (2002)] that 3-spin models are in the same universality class as an Ising spin glass in a magnetic field. However, slightly in the non-mean-field region, we find an apparent transition in the 3-spin model, in contrast to results for the Ising spin glass in a field. This may indicate that even larger sizes are needed to probe the asymptotic behavior in this region.