Abstract
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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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)
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)
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)
Duneau, M., Souillard, B., Iagolnitzer, D.: Decay of correlations for infinite-range interactions. J. Math. Phys.16, 1662–1666 (1975)
Fisher, M.E.: On discontinuity of the pressure. Commun. Math. Phys.26, 6–14 (1972)
Gallavotti, G., Miracle-Sole, S.: Correlation functions of a lattice system. Commun. Math. Phys.7, 274–288 (1968)
Griffiths, R., Ruelle, D.: Strict convexity (continuity) of the pressure in lattice systems. Commun. Math. Phys.23, 169–175 (1971)
Holley, R.A., Stroock, D.W.: Applications of the stochastic Ising model to the Gibbs states. Commun. Math. Phys.48, 249–265 (1976)
Holsztynski, W., Slawny, J.: Peierls condition and the number of ground states. Commun. Math. Phys.61, 177–190 (1978)
Israel, R.B.: Existence of phase transitions for long-range interactions. Commun. Math. Phys.43, 59–68 (1975)
Israel, R.B.: High temperature analyticity in classical lattice systems. Commun. Math. Phys.50, 245–257 (1976)
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
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)
Pirogov, S.A., Sinai, Ya.G.: Phase diagrams of classical lattice systems. Theor. Math. Phys.25, 358–369 (1975)
Pirogov, S.A., Sinai, Ya.G.: Ground states in two-dimensional Boson quantum field theory. Ann. Phys.109, 393–400 (1977)
Ruelle, D.: Statistical mechanics, New York: Benjamin 1969
Ruelle, D.: Thermodynamic Formalism. Reading, Mass.: Addison-Wesley 1978
Sylvester, G.S.: Weakly coupled Gibbs measures. Preprint, Rockefeller University (1977)
Vasershtein, L.N.: Markov processes over denumerable products of spaces, describing large systems of automata. Probl. Trans. Inf.5, 64–72 (1969) (English Translation)
Duneau, M., Souillard, B.: Cluster properties of lattice and continuous systems. Commun. Math. Phys.47, 155–166 (1976)
Iagolnitzer, D., Souillard, B.: Decay of correlations for slowly decreasing potentials. Phys. Rev. A16, 1700–1704 (1977)
Iagolnitzer, D., Souillard, B.: On the analyticity in the potential in classical statistical mechanics. Commun. Math. Phys.60, 131–152 (1978)
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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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DOI: https://doi.org/10.1007/BF01562538