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Journal of Statistical Physics

, Volume 97, Issue 1–2, pp 87–144 | Cite as

On the Ising Model with Strongly Anisotropic External Field

  • F. R. Nardi
  • E. Olivieri
  • M. Zahradník
Article

Abstract

In this paper we analyze the equilibrium phase diagram of the two-dimensional ferromagnetic n.n. Ising model when the external field takes alternating signs on different rows. We show that some of the zero-temperature coexistence lines disappear at every positive sufficiently small temperature, whereas one (and only one) of them persists for sufficiently low temperature.

Ising model anisotropic field phase diagram cluster expansion 

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REFERENCES

  1. [BKL]
    J. Bricmont, K. Kuroda, and J. L. Lebowitz, First order phase transitions in lattice and continuous systems: Extension of Pirogov-Sinai theory, Comm. Math. Phys. 101:501-538 (1985).Google Scholar
  2. [D]
    R. L. Dobrushin, Estimates of semi-invariants for the Ising model at low temperatures topics in statistical and theoretical physics, Amer. Math. Soc. Transl. (2) V 177:59-81 (1996).Google Scholar
  3. [DMS]
    E. I. Dinaburg, A. E. Mazel, and Ya. G. Sinai, The ANNNI model and contour models with interaction, Soviet Scientific Reviews C, Vol. 6, S. P. Novikov, ed. (Gordon and Breach, New York, 1987), pp. 113-168.Google Scholar
  4. [DO]
    R. L. Dobrushin, Existence of a phase transition in the two-dimensional and three-dimensional Ising models, Sov. Phys. Dokl. 10:111-113 (1965).Google Scholar
  5. [DS]
    E. I. Dinaburg and Ya. G. Sinai, An analysis of ANNNI model by Peierls contour method, Comm. Math. Phys. 98:119-144 (1985).Google Scholar
  6. [DS1]
    E. I. Dinaburg and Ya. G. Sinai, Contour models with interaction and their applications, Sel. Math. Sov. 7:291-315 (1988).Google Scholar
  7. [GMM]
    G. Gallavotti, A. Martin Löf, and Miracle Sole, Battelle Seattle (1971) Rendecontres, A. Lenard, ed., Lecture Notes in Physics, Vol. 20 (Springer, Berlin, 1973), pp. 162-204.Google Scholar
  8. [GR]
    R. B. Griffiths, Peierls' proof of spontaneous magnetization of a two-dimensional Ising ferrogmagnet, Phys. Rev. A 136:437-439 (1964).Google Scholar
  9. [HZ]
    P. Holický and M. Zahradník, Stratified low temperature phases of stratifies spin models. A general P. S. approach, submitted.Google Scholar
  10. [KP]
    R. Kotecký and D. Preiss, Cluster expansions for abstract polymer models, Comm. Math. Phys. 103:491-498 (1996).Google Scholar
  11. [NaO]
    F. R. Nardi and E. Olivieri, Low temperature stochastic dynamics for an Ising model with alternating field, Markov Proc. Rel. Field 2:117-166 (1996).Google Scholar
  12. [P]
    R. Peierls, On the Ising model of ferromagnetism, Proc. Cambridge Phil. Soc. 32:477-482 (1936).Google Scholar
  13. [PS]
    S. A. Pirogov and Ya. G. Sinai, Phase diagrams of classical lattice systems, Theor. Math. Phys. 25, 26:1185-1192, 39-49 (1975, 1976).Google Scholar
  14. [S]
    Ya. G. Sinai, Theory of phase transitions. Rigorous results (Pergamon Press, 1982).Google Scholar
  15. [Z]
    M. Zahradník, An alternate version of Pirogov-Sinai theory, Comm. Math. Phys. 93:559-581 (1984).Google Scholar
  16. [ZR]
    M. Zahradník, A short course on the Pirogov-Sinai theory, Rendiconti di Matematica 18:1-75 (1998).Google Scholar

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • F. R. Nardi
    • 1
  • E. Olivieri
    • 1
  • M. Zahradník
    • 2
  1. 1.Dipartimento di MatematicaII Università di Roma Tor VergataRomeItaly
  2. 2.Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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