Abstract
We consider geometrically disordered systems with a continuous symmetry groupG, where the internal degrees of freedom are attached to the vertices of a graph. We show that equilibrium states remainG-invariant at any temperatureT>0 if a random walk on the graph is recurrent. This generalizes a previous result obtained by Cassi.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Cassi,Phys. Rev. Lett. 68:3631 (1992).
N. D. Mermin and H. Wagner,Phys. Rev. Lett. 17:1133 (1966).
N. D. Mermin,J. Math. Phys. 8:1061 (1967).
H. Araki,Commun. Math. Phys. 44:1 (1975).
R. L. Dobrushin and S. B. Shlosman,Commun. Math. Phys. 42:31 (1975).
C. E. Pfister,Commun. Math. Phys. 79:181 (1981).
J. Fröhlich and C. E. Pfister,Commun. Math. Phys. 81:277 (1981).
N. Th. Varopoulos,J. Funct. Anal. 63:215 (1985).
P. Billingsley,Probability and Measure (Wiley, New York, 1986), p. 38, Theorem 3.3.
C. A. Bonato, J. Fernando Perez, and A. Klein,J. Stat. Phys. 29:159 (1982).
H.-O. Georgii,Gibbs Measures and Phase Transitions (de Gruyter, Berlin, 1988), p. 170, Proposition 9.3.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Merkl, F., Wagner, H. Recurrent random walks and the absence of continuous symmetry breaking on graphs. J Stat Phys 75, 153–165 (1994). https://doi.org/10.1007/BF02186284
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02186284