title: Finite-size critical scaling in Ising spin glasses in the mean-field regime.
abstract: We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida-Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida-Thouless transition even though it is absent.
authors.affiliation: Felix Bernstein Inst. Math. Stat. Biosci., Göttingen, Germany.|Univ. Göttingen, Inst. Math. Stochast., D-37073 Göttingen, Germany.|Max Planck Inst. Biophys. Chem., Stat. Inverse Problems Biophys. Grp., D-37077 Göttingen, Germany.
authors.forename: T
authors.initials: T
authors.lastname: Aspelmeier
authors.affiliation: Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA.|Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.|Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, England.
authors.forename: Helmut G
authors.initials: HG
authors.lastname: Katzgraber
authors.affiliation: Department of Physics, University of California, Santa Cruz, California 95064, USA.
authors.forename: Derek
authors.initials: D
authors.lastname: Larson
authors.affiliation: School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom.
authors.forename: M A
authors.initials: MA
authors.lastname: Moore
authors.affiliation: Department of Physics, University of California, Santa Cruz, California 95064, USA.
authors.forename: Matthew
authors.initials: M
authors.lastname: Wittmann
authors.affiliation: Division of Quantum Phases and Devices, School of Physics, Konkuk University, Seoul 143-701, Korea.
authors.forename: Joonhyun
authors.initials: J
authors.lastname: Yeo