Percolation for low energy clusters and discrete symmetry breaking in classical spin systems |
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Authors: | Hans-Otto Georgii |
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Institution: | (1) Fakultät für Mathematik, Abt. 1, Universität Bielefeld, D-4800 Bielefeld, Federal Republic of Germany;(2) Present address: Mathematisches Institut der Universität, Theresienstraße 39, D-8000 München 2, Federal Republic of Germany |
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Abstract: | We consider classical lattice systems in two or more dimensions with general state space and with short-range interactions. It is shown that percolation is a general feature of these systems: If the temperature is sufficiently low, then almost surely with respect to some equilibrium state there is an infinite cluster of spins trying to form a ground state. For systems having several stable sets of symmetry-related ground states we show that at low temperatures spontaneous symmetry breaking occurs because in a two-dimensional subsystem there is a unique infinite cluster of this type. |
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