Journal of Statistical Physics

, Volume 70, Issue 5–6, pp 1391–1400 | Cite as

Absence of first-order phase transitions for antiferromagnetic systems

  • David Klein
  • Wei-Shih Yang
Short Communications


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.

Key words

Phase transition antiferromagnet Gibbs state free energy pressure Ising model 


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  1. 1.
    M. Aizenman, Translation invariance and instability of phase coexistence in the two-dimensional Ising system,Commun. Math. Phys. 73:83–94 (1980).Google Scholar
  2. 2.
    R. M. Burton and M. Keane, Density and uniqueness in percolation,Commun. Math. Phys. 121:501–505 (1989).Google Scholar
  3. 3.
    G. Choquet and P.-A. Meyer, Existence et unicité des représentations intégrales dans les convexes compacts quelconques,Ann. Inst. Fourier 13:139–154 (1963).Google Scholar
  4. 4.
    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).Google Scholar
  5. 5.
    R. L. Dobrushin, J. Kolafa, and S. B. Shlosman, Phase diagram of the two-dimensional Ising antiferromagnet,Commun. Math. Phys. 102:89–103 (1985).Google Scholar
  6. 6.
    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).Google Scholar
  7. 7.
    C. Preston,Random Fields (Springer-Verlag, 1976).Google Scholar
  8. 8.
    L. K. Runnells, Lattice gas theories of melting, inPhase Transitions and Critical Phenomena, Vol. 2, Domb and Green, eds. (Academic Press, 1972).Google Scholar
  9. 9.
    L. Russo, The infinite cluster method in the two-dimensional Ising model,Commun. Math. Phys. 67:251–266 (1979).Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • David Klein
    • 1
  • Wei-Shih Yang
    • 2
  1. 1.Department of MathematicsCalifornia State UniversityNorthridge
  2. 2.Department of MathematicsTemple UniversityPhiladelphia

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