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Critical Exponents of the Three-Dimensional Ising Spin Glass

H.G. Ballesteros, Andrés De la Cruz, L. A. Fernández, Víctor Martín-Mayor, J. Pech, Juan Jesus Ruiz-Lorenzo, Alfonso Tarancón, Pedro Téllez, C.L. Ullod, C. Ungil

Published Jun 13, 2000• 0 citations
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We propose a numerical criterion which can be used to obtain accurate and reliable values of the ordering temperatures and critical exponents of spin glasses. Using this method we find a value of the ordering temperature for the $\ifmmode\pm\else\textpm\fi{}J$ Ising spin glass in three dimensions which is definitely nonzero and in good agreement with previous estimates. We show that the critical exponents of three-dimensional Ising spin glasses do not obey the usual universality rules.
We compare simulation data from different sources on two canonical three-dimensional Ising spin glasses (ISGs): the binomial $\ifmmode\pm\else\textpm\fi{}J$ near-neighbor interaction ISG and the Gaussian interaction ISG. We allow for the possibility of corrections to finite size scaling and estimate the correction exponent w. Consistent estimates for the critical temperatures Tg{T}_{g}Tg​ and for the critical exponents for each system are obtained. The data strongly indicate that critical exponents in the two systems are significantly different from each other. These results thus confirm a breakdown of standard universality rules in Ising spin glasses.
The three-dimensional nearest-neighbor Ising spin-glass model with Gaussian bonds (〈J2{J}^{2}J2〉=1) is studied numerically using the ``large-cell'' renormalization group. Estimates for the critical coupling and the thermal exponent are Kc{K}_{c}Kc​=1/Tc{T}_{c}Tc​=1.2\ifmmode\pm\else\textpm\fi{}0.1 and yt{y}_{t}yt​=1/\ensuremath{\nu}=0.30\ifmmode\pm\else\textpm\fi{}0.05, respectively.