Dynamics in the Sherrington-Kirkpatrick Ising spin glass at and above Tg

Abstract

A detailed numerical study is made of relaxation at equilibrium in the Sherrington-Kirkpatrick Ising spin glass model, at and above the critical temperature Tg. The data show a long time stretched exponential relaxation q(t) ~ exp[-(t/tau(T))^beta(T)] with an exponent beta(T) tending to ~ 1/3 at Tg. The results are compared to those which were observed by Ogielski in the 3d ISG model, and are discussed in terms of a phase space percolation transition scenario.

6 pages, 7 figures

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• Laplacian spectra of complex networks and random walks on them: Are scale-free architectures really important?
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• On the Question of Ergodicity in Quantum Spin Glass Phase and its role in Quantum Annealing
• Stretched exponential behavior and random walks on diluted hypercubic lattices
• Numerical study of the dynamics of some long range spin glass models