Deterministic spin models with a glassy phase transition

Abstract

We consider the infinite-range deterministic spin models with Hamiltonian $H={\sum }_{i,j=1}^N{J}_{i,j}{\sigma }_i{\sigma }_j$, where $J$ is the quantization of a chaotic map of the torus. The mean field (TAP) equations are derived by summing the high temperature expansion. They predict a glassy phase transition at the critical temperature $T\sim 0.8$.

8 pages, no figures, RevTex format

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Cited by in corpus (2)

• Statistics of energy levels and zero temperature dynamics for deterministic spin models with glassy behaviour
• A large-N approximated field theory for multipartite entanglement