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Название: Recurrent Random Walks and the Absence of Continuous Symmetry Breaking on Graphs
Авторы: Merkl F., Wagner H.
We consider geometrically disordered systems with a continuous symmetry group G, where the internal degrees of freedom are attached to the vertices of a graph. We show that equilibrium states remain G-invariant at any temperature T > 0 if a random walk on the graph is recurrent. This generalizes a previous result obtained by Cassi.