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

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.

8 pages, 9 figures, 1 table

References in corpus (6)

• The critical behavior of three-dimensional Ising spin glass models
• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
• Diluted one-dimensional spin glasses with power law decaying interactions
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Ising spin glass transition in magnetic field out of mean-field
• Interface free energies in p-spin glass models

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