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The European Physical Journal B

Equivalence of random and competing nonrandom bonds for Edwards Anderson spin-glass

Fritz Haake, Maciej Lewenstein, Martin Wilkens

Published Jun 1, 1987• 3 citations
Publisher
DOI
10.1007/bf01311656

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By mapping the Edwards-Anderson model onto a nonrandom Ising model we argue that the lower critical dimension ${d}^{*}$ for the Edwards-Anderson spin-glass is close to 3 and may depend on the probability distribution of the bond strengths. For $d>{d}^{*}$, the approach to spin-glass order from the paramagnetic phase is characterized by Ising exponents. At $d={d}^{*}$, however, the critical exponents defined for $T>{T}_{c}$ are twice the corresponding Ising ones. These results are consistent with recent computer simulations.

Physical Review Letters•Dec 2, 1985•9 citations
By mapping the Edwards-Anderson model onto a nonrandom Ising model we argue that the lower critical dimension d∗{d}^{*}d∗ for the Edwards-Anderson spin-glass is close to 3 and may depend on the probability distribution of the bond strengths. For d>d∗d>{d}^{*}d>d∗, the approach to spin-glass order from the paramagnetic phase is characterized by Ising exponents. At d=d∗d={d}^{*}d=d∗, however, the critical exponents defined for T>TcT>{T}_{c}T>Tc​ are twice the corresponding Ising ones. These results are consistent with recent computer simulations.