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arXiv · 0712.2658

Dynamics of an Ising Spin Glass on the Bethe Lattice

Martin Kiemes·Heinz Horner
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Abstract

We study the dynamical low temperature behaviour of the Ising spin glass on the Bethe lattice. Starting from Glauber dynamics we propose a cavity like Ansatz that allows for the treatment of the slow (low temperature) part of dynamics. Assuming a continuous phase transitions and ultrametricity with respect to long time scales we approach the problem perturbatively near the critical temperature. The theory is formulated in terms of correlation-response-functions of arbitrary order. They can, however, be broken down completely to products of pair functions depending on two time arguments only. For binary couplings $J=\pm I$ a spin glass solution is found which approaches the corresponding solution for the SK-model in the limit of high connectivity. For more general distributions $P(J)$ no stable or marginal solution of this type appears to exist. The nature of the low temperature phase in this more general case is unclear.

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Martin Kiemes, Heinz Horner. 2007-12-17. Dynamics of an Ising Spin Glass on the Bethe Lattice. https://doi.org/10.1088/1751-8113/41/32/324017

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