98-674 Georgii, H.-O.

Translation invariance and continuous symmetries in two-dimensional continuum systems (39K, LaTeX 2e) Oct 22, 98

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Abstract. We reconsider the problem of absence of continuous symmetry breaking for systems of point particles in $\R^2$. Assuming smoothness and suitable decay of the interaction, we show that each tempered Gibbs measure is invariant under translations. If the particles exhibit internal degrees of freedom with continuous symmetries, the latter are also preserved. The proof is elementary and avoids the use of superstability estimates.

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