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Variations of the Mermin--Wagner theorem

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The Mermin—Wagner theorem originates from theoretical physics; in its initial form it states that two-dimensional systems of statistical mechanics do not exhibit a continuous symmertry breakdown. In modern terms, the theorem asserts that for random fields with continuous values on bi-dimensional graphs, if the conditional probabilities of the field are invariant under a continuous transformation group then the field itself is invariant under the same group. Also, for point random fields in a plane, if the conditional probabilities are invariant under space-shifts then the field itself is shift-invariant. (Most recent results in this direction belong to T Richthammer.)

The talk will focus on modifications of the above theorems covering various classes of systems in quantum statistical mechanics. No preliminary knowledge from Quantum Mechanics will be assumed.

This talk is part of the Probability series.

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