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Binder Parameter of a Heisenberg Spin-Glass Model in Four Dimensions

Takayuki Shirakura·Fumitaka Matsubara
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Abstract

We studied the phase transition of the $\pm J$ Heisenberg model with and without a random anisotropy on four dimensional lattice $L\times L\times L\times (L+1)$ $(L\leq 9)$. We showed that the Binder parameters $g(L,T)$'s for different sizes do not cross even when the anisotropy is present. On the contrary, when a strong anisotropy exists, $g(L,T)$ exhibits a steep negative dip near the spin-glass phase transition temperature $T_{\rm SG}$ similarly to the $p-$state infinite-range Potts glass model with $p \geq 3$, in which the one-step replica-symmetry-breaking (RSB) occurs. We speculated that a one-step RSB-like state occurs below $T_{\rm SG}$, which breaks the usual crossing behavior of $g(L,T)$.

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Takayuki Shirakura, Fumitaka Matsubara. 2002-11-23. Binder Parameter of a Heisenberg Spin-Glass Model in Four Dimensions. https://doi.org/10.1103/physrevb.67.100405

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