We revisited, by means of numerical simulations, the one-dimensional bond diluted Levy Ising spin glasses outside the limit of validity of mean-field theories. In these models the probability that two spins at distance rinteract (via disordered interactions, Jij=±1) decays as r−ρ. We have estimated, using finite size scaling techniques, the infinite volume correlation length and spin glass susceptibility for ρ=5/3and ρ=9/5. We have obtained strong evidence for divergences of the previous observables at a nonzero critical temperature. We discuss the behavior of the critical exponents, especially when approaching the value ρ=2, corresponding to a critical threshold beyond which the model has no phase transition. Finally, we numerically study the model right at the threshold value ρ=2.
Infinite volume extrapolation in the one-dimensional bond diluted Levy spin-glass model near its lower critical dimension / L., Leuzzi; Parisi, Giorgio; RICCI TERSENGHI, Federico; J. J., Ruiz Lorenzo. - In: PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS. - ISSN 1098-0121. - 91:(2015), p. 064202. [10.1103/PhysRevB.91.064202]
Infinite volume extrapolation in the one-dimensional bond diluted Levy spin-glass model near its lower critical dimension
PARISI, Giorgio;RICCI TERSENGHI, Federico;
2015
Abstract
We revisited, by means of numerical simulations, the one-dimensional bond diluted Levy Ising spin glasses outside the limit of validity of mean-field theories. In these models the probability that two spins at distance rinteract (via disordered interactions, Jij=±1) decays as r−ρ. We have estimated, using finite size scaling techniques, the infinite volume correlation length and spin glass susceptibility for ρ=5/3and ρ=9/5. We have obtained strong evidence for divergences of the previous observables at a nonzero critical temperature. We discuss the behavior of the critical exponents, especially when approaching the value ρ=2, corresponding to a critical threshold beyond which the model has no phase transition. Finally, we numerically study the model right at the threshold value ρ=2.File | Dimensione | Formato | |
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