Abstract

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.