Abstract
New proofs are given for Propositions 1 and 2 of C. C. Wu,J. Stat. Phys. 50:251 (1996). The propositions involved upper and lower bounds on the critical temperature for these models. Besides being more direct than the previous proofs, the new proofs improve both bounds.
References
C. C. Wu, Ising Models on Hyperbolic Graphs,J. Stat. Phys. 50:251 (1996).
T. P. Eggarter, Cayley trees, the Ising problem, and the thermodynamic limit,Phys. Rev. B. 9:2989 (1974).
C. J. Thompson, Local properties of an Ising model on a Cayley tree,J. Stat. Phys. 27:441 (1982).
R. B. Griffiths, Correlations in Ising ferromagnets I and II,J. Math. Phys. 8:478, 484 (1967).
D. G. Kelly, and S. Sherman, General Griffiths Inequalities on correlations in Ising ferromagnets,J. Math. Phys 9:313 (1968).
G. S. Sylvester, Inequalities for continuous spin Ising ferromagnets,J. Stat. Phys. 15:327 (1976).
J. L. Monroe, Upper bounds on the critical temperature for various Ising models,J. Stat. Phys. 40:249 (1985).
Author information
Authors and Affiliations
Additional information
Communicated by J. L. Lebowitz
Rights and permissions
About this article
Cite this article
Monroe, J.L. Comment on: Ising models on hyperbolic graphs. J Stat Phys 88, 513–518 (1997). https://doi.org/10.1007/BF02508482
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02508482