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Decay of correlations in classical lattice models at high temperature

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In classical statistical mechanical lattice models with many body potentials of finite or infinite range and arbitrary spin it is shown that the truncated pair correlation function decays in the same weighted summability sense as the potential, at high temperature.

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References

  1. Dobrushin, R.L.: The description of a random field by means of conditional probabilities and conditions of its regularity. Theory Probab. Its. Appl.13, 197–224 (1968)

    Google Scholar 

  2. Dobrushin, R.L.: The problem of uniqueness of a Gibbsian random field and the problem of phase transitions. Funct. Anal. Its Appl.2, 302–312 (1968)

    Google Scholar 

  3. Dobrushin, R.L., Nakhapetyan, B.S.: Strong convexity of the pressure for lattice systems of classical statistical physics. Theor. Math. Phys.20, 782–790 (1974)

    Google Scholar 

  4. Duneau, M., Souillard, B., Iagolnitzer, D.: Decay of correlations for infinite-range interactions. J. Math. Phys.16, 1662–1666 (1975)

    Google Scholar 

  5. Fisher, M.E.: On discontinuity of the pressure. Commun. Math. Phys.26, 6–14 (1972)

    Google Scholar 

  6. Gallavotti, G., Miracle-Sole, S.: Correlation functions of a lattice system. Commun. Math. Phys.7, 274–288 (1968)

    Google Scholar 

  7. Griffiths, R., Ruelle, D.: Strict convexity (continuity) of the pressure in lattice systems. Commun. Math. Phys.23, 169–175 (1971)

    Google Scholar 

  8. Holley, R.A., Stroock, D.W.: Applications of the stochastic Ising model to the Gibbs states. Commun. Math. Phys.48, 249–265 (1976)

    Google Scholar 

  9. Holsztynski, W., Slawny, J.: Peierls condition and the number of ground states. Commun. Math. Phys.61, 177–190 (1978)

    Google Scholar 

  10. Israel, R.B.: Existence of phase transitions for long-range interactions. Commun. Math. Phys.43, 59–68 (1975)

    Google Scholar 

  11. Israel, R.B.: High temperature analyticity in classical lattice systems. Commun. Math. Phys.50, 245–257 (1976)

    Google Scholar 

  12. Lanford, O.E. III: Entropy and equilibrium states in classical statistical mechanics. In: Lecture notes in physics, Vol. 20. Statistical mechanics and mathematical problems, Lenard, A. (ed.). Berlin, Heidelberg, New York: Springer 1973

    Google Scholar 

  13. Lanford, O.E. III, Ruelle, D.: Observables at infinity and states with short range correlations in statistical mechanics. Commun. Math. Phys.13, 194–215 (1969)

    Google Scholar 

  14. Pirogov, S.A., Sinai, Ya.G.: Phase diagrams of classical lattice systems. Theor. Math. Phys.25, 358–369 (1975)

    Google Scholar 

  15. Pirogov, S.A., Sinai, Ya.G.: Ground states in two-dimensional Boson quantum field theory. Ann. Phys.109, 393–400 (1977)

    Google Scholar 

  16. Ruelle, D.: Statistical mechanics, New York: Benjamin 1969

    Google Scholar 

  17. Ruelle, D.: Thermodynamic Formalism. Reading, Mass.: Addison-Wesley 1978

    Google Scholar 

  18. Sylvester, G.S.: Weakly coupled Gibbs measures. Preprint, Rockefeller University (1977)

  19. Vasershtein, L.N.: Markov processes over denumerable products of spaces, describing large systems of automata. Probl. Trans. Inf.5, 64–72 (1969) (English Translation)

    Google Scholar 

  20. Duneau, M., Souillard, B.: Cluster properties of lattice and continuous systems. Commun. Math. Phys.47, 155–166 (1976)

    Google Scholar 

  21. Iagolnitzer, D., Souillard, B.: Decay of correlations for slowly decreasing potentials. Phys. Rev. A16, 1700–1704 (1977)

    Google Scholar 

  22. Iagolnitzer, D., Souillard, B.: On the analyticity in the potential in classical statistical mechanics. Commun. Math. Phys.60, 131–152 (1978)

    Google Scholar 

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Communicated by E. Lieb

Research partially supported by the National Science Foundation under Grant MCS 78-00680

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Gross, L. Decay of correlations in classical lattice models at high temperature. Commun.Math. Phys. 68, 9–27 (1979). https://doi.org/10.1007/BF01562538

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