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Percolation for low energy clusters and discrete symmetry breaking in classical spin systems

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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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  1. Hans-Otto Georgii

    Present address: Mathematisches Institut der Universität, Theresienstraße 39, D-8000, München 2, Federal Republic of Germany

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  1. Fakultät für Mathematik, Abt. 1, Universität Bielefeld, D-4800, Bielefeld, Federal Republic of Germany

    Hans-Otto Georgii

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  1. Hans-Otto Georgii
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Communicated by E. Lieb

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Georgii, HO. Percolation for low energy clusters and discrete symmetry breaking in classical spin systems. Commun.Math. Phys. 81, 455–473 (1981). https://doi.org/10.1007/BF01208268

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  • DOI: https://doi.org/10.1007/BF01208268

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