We test for the existence of a spin-glass phase transition, the de Almeida-Thouless line, in an externally applied (random) magnetic field by performing Monte Carlo simulations on a power-law diluted one-dimensional Ising spin glass for very large system sizes. We find that a de Almeida-Thouless line occurs only in the mean-field regime, which corresponds, for a short-range spin glass, to dimension d larger than 6.

arXiv:0812.0421Physical Review LettersApr 30, 2009103 citations

Journal of Superconductivity and Novel Magnetism

Monte Carlo Simulation of 2D Ising Spin Glass with Power Law Decaying Interactions

Habte Dulla Berry, Pooran Singh

Published Dec 17, 2012• 2 citations

Publisher

DOI: 10.1007/s10948-012-1908-3

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The remanent magnetization

{M}_{r}

and the excess energy \ensuremath{\Delta}E are studied for the Sherrington-Kirpatrick model of spin glasses using Monte Carlo simulations. At zero temperature T the system relaxes to a stationary nonequilibrium state with nonzero

{M}_{r}

and \ensuremath{\Delta}E; both quantities are self-averaging. For 0

{T}_{c}

the simulations indicate that

{M}_{r}

and \ensuremath{\Delta}E decay to zero as a power law in time.