Soft Matter and Complex Systems Seminar

The well-known Mermin-Wagner theorem tells that in the lattice spin systems possessing continuous symmetry, for lattice dimensions 1 and 2, there is no long-range order at positive temperatures. The aim of the talk is to review an extension (after A. Auerbach et al.) of this theorem to the zero-temperature case: the ground state is not ordered if there is an energy gap over the ground state.