Abstract
We consider a spin system with nearest-neighbor antiferromagnetic pair interactions in a two-dimensional lattice. We prove that the free energy of this system is differentiable with respect to the uniform external fieldh, for all temperatures and allh. This implies the absence of a first-order phase transition in this system.
This is a preview of subscription content, log in via an institution to check access.
References
M. Aizenman, Translation invariance and instability of phase coexistence in the two-dimensional Ising system,Commun. Math. Phys. 73:83–94 (1980).
R. M. Burton and M. Keane, Density and uniqueness in percolation,Commun. Math. Phys. 121:501–505 (1989).
G. Choquet and P.-A. Meyer, Existence et unicité des représentations intégrales dans les convexes compacts quelconques,Ann. Inst. Fourier 13:139–154 (1963).
R. L. Dobrushin, The problem of uniqueness of a Gibbsian random field and the problem of phase transitions,Funct. Anal. Appl. 2:302–312 (1968).
R. L. Dobrushin, J. Kolafa, and S. B. Shlosman, Phase diagram of the two-dimensional Ising antiferromagnet,Commun. Math. Phys. 102:89–103 (1985).
A. Gandolfi, M. Keane, and L. Russo, On the uniqueness of the infinite occupied cluster in dependent two-dimensional site percolation,Ann. Prob. 16:1147–1157 (1988).
C. Preston,Random Fields (Springer-Verlag, 1976).
L. K. Runnells, Lattice gas theories of melting, inPhase Transitions and Critical Phenomena, Vol. 2, Domb and Green, eds. (Academic Press, 1972).
L. Russo, The infinite cluster method in the two-dimensional Ising model,Commun. Math. Phys. 67:251–266 (1979).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Klein, D., Yang, WS. Absence of first-order phase transitions for antiferromagnetic systems. J Stat Phys 70, 1391–1400 (1993). https://doi.org/10.1007/BF01049441
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01049441