Critical Point Scaling of Ising Spin Glasses in a Magnetic Field

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 $R=t/H^{2/\Delta }$ 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 $1/(\xi H^{4/(d+2-\eta )})\sim f(R)$. 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.

arXiv comment9 pages, 8 figures

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Cited by in corpus (9)

• Finite-size critical scaling in Ising spin glasses in the mean-field regime
• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• Physical observables of the Ising spin glass in 6-epsilon dimensions: asymptotical behavior around the critical fixed point
• Spin-glass dynamics: experiment, theory and simulation
• Evidence that the AT transition disappears below six dimensions
• Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field
• Comment on "Critical point scaling of Ising spin glasses in a magnetic field" by J. Yeo and M.A. Moore
• Reply to "Comment on "Critical Point Scaling of Ising Spin Glasses in a Magnetic Field" "
• Evidence of de Almeida-Thouless line below six dimensions