Abstract
Using local Ward identities and a new correlation inequality, we prove that the mean field transition temperature is an upper bound on the true transition temperature in multicomponent Heisenberg-type classical ferromagnets.
Similar content being viewed by others
References
H. Brascamp and E. Lieb, inFunctional Integration and Its Applications, A. Arthurs, ed. (Clarendon Press, Oxford, 1975).
M. Cassandro, E. Olivieri, A. Pellegrinotti, and E. Presutti,Z. Wahrs. v. Geb. 41:313 (1978).
R. L. Dobrushin,Theory Prob. Appl. 15:458 (1970).
W. Driessler, L. Landau, and J. Fernando-Perez,J. Stat. Phys. 20:123 (1979).
F. Dyson, E. Lieb, and B. Simon,J. Stat. Phys. 18:335 (1978).
J. Frohlich, R. Israel, E. Lieb, and B. Simon,Commun. Math. Phys. 62:1 (1978).
J. Ginibre,Commun. Math. Phys. 16:310 (1979).
R. Griffiths,Commun. Math. Phys. 6:121 (1967).
R. Israel,Commun. Math. Phys. 50:245 (1976).
B. Simon,Commun. Math. Phys. 68:183 (1979).
Author information
Authors and Affiliations
Additional information
Research partially supported by the NSF under Grant MCS-78-01885.
Rights and permissions
About this article
Cite this article
Simon, B. Mean field upper bound on the transition temperature in multicomponent ferromagnets. J Stat Phys 22, 491–493 (1980). https://doi.org/10.1007/BF01012868
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01012868