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Infinitely many states and stochastic symmetry in a Gaussian Potts-Hopfield model. (English) Zbl 1002.82008

Summary: We study a Gaussian Potts-Hopfield model. Whereas for Ising spins and two disorder variables per site the chaotic pair scenario is realized, we find that for \(q\)-state Potts spins \(q(q-1)\)-tuples occur. Beyond the breaking of a continuous stochastic symmetry, we study the fluctuations and obtain the Newman-Stein metastate description for our model.

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
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