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arXiv · 1412.2448

Critical Point Scaling of Ising Spin Glasses in a Magnetic Field

Joonhyun Yeo·M. A. Moore
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Abstract

Critical point scaling in a field $H$ applies for the limits $t\to 0$, (where $t=T/T_c-1$) and $H\to 0$ but with the ratio $R=t/H^{2/Δ}$ finite. $Δ$ is a critical exponent of the zero-field transition. We study the replicon correlation length $ξ$ and from it the crossover scaling function $f(R)$ defined via $1/(ξH^{4/(d+2-η)}) \sim f(R)$. 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 $d \le 6$ 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 $d \le 6$, which we review.

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BibTeXRIS

Joonhyun Yeo, M. A. Moore. 2015-03-31. Critical Point Scaling of Ising Spin Glasses in a Magnetic Field. https://doi.org/10.1103/physrevb.91.104432

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