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Article

A quantum Mermin-Wagner theorem for quantum rotators on two-dimentional graph

Journal of Mathematical Physics. 2013. Vol. 54. No. 3.
Kelbert M., Suhov Y.

We study symmetry properties of quantum systems over 2D graphs or manifolds, with continuous spins, in the spirit

of the Mermin-Wagner' theorem. In the model of quantum rotators the phase space of a single spin is a d-dimensional

torus, and spins (or particles) are attached to sites of a graph satisfying a special bi-dimensional property. We construct

the so-called infinite-volume Gibbs state, with or without boundary conditions. Next, we study the problem of preserving

or spontaneous breaking of continuous symmetry.