- 98-674 Georgii, H.-O.
- Translation invariance and continuous symmetries in two-dimensional
(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.