Abstract
For a one-dimensional array ofS N−1 spins (N ⩾ 2) with isotropic pair interactions (and more general systems) with J(j−i) obeying supn[n−1∑ n1 j 2|J(j)|]<∞, we prove that every equilibrium state is invariant under the natural action ofSO(N). In particular, there is no long-range order of the conventional type. Included is the caseJ(n)=n −2.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. J. Dyson,Commun. Math. Phys. 12:212 (1969).
F. J. Dyson,Commun. Math. Phys. 21:269 (1971).
J. Frohlich, R. Israel, E. Lieb, and B. Simon,Commun. Math. Phys. 62:1 (1978).
J. Frohlich and T. Spencer, Bures preprint.
C. Pfister, Ecole Polytechnique Fédérale, preprint.
J. Rogers and C. Thompson,J. Stat. Phys.,25:669.
D. Ruelle,Commun. Math. Phys. 9:267 (1968).
B. Simon and A. Sokal,J. Stat. Phys.,25:679.
Author information
Authors and Affiliations
Additional information
Research partially supported by U.S.N.S.F. Grant No. MCS-78-01885.
S. Fairchild Scholar at Caltech. On leave from Departments of Mathematics and Physics, Princeton University, Princeton, New Jersey 08544.
Rights and permissions
About this article
Cite this article
Simon, B. Absence of continuous symmetry breaking in a one-dimensional n−2 model. J Stat Phys 26, 307–311 (1981). https://doi.org/10.1007/BF01013173
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01013173