Critical point scaling of Ising spin glasses in a magnetic field

Article

关键词: RENORMALIZATION-GROUP;    ORDER-PARAMETER;    PHASE;    TRANSITION;    MODEL;    DIMENSIONS;    SYMMETRY;    BEHAVIOR;   

DOI  :  10.1103/PhysRevB.91.104432

来源: SCIE

【 摘 要 】

Critical point scaling in a field H applies for the limits t -> 0 (where t = T/T-c - 1) and H -> 0 but with the ratio R = t/H-2/Delta finite. Delta is a critical exponent of the zero-field transition. We study the replicon correlation length xi and from it the crossover scaling function f (R) defined via 1/(xi H4/(d+2-eta)) similar to f (R). We have calculated analytically f (R) for the mean-field limit of the Sherrington-Kirkpatrick model. In dimension d = 3, we have determined the exponents and the critical scaling function f (R) within two versions of the Migdal-Kadanoff (MK) renormalization group procedure. One of the MK versions gives results for f (R) in d = 3 in reasonable agreement with those of the Monte Carlo simulations at the values of R for which they can be compared. If there were a de Almeida-Thouless (AT) line for d <= 6, it would appear as a zero of the function f (R) at some negative value of R, but there is no evidence for such behavior. This is consistent with the arguments that there should be no AT line for d <= 6, which we review.

【 授权许可】

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