Abstract
We deduce an integral equation for the infinite volume correlation functions of a class of lattice systems and we apply it to find results on the analyticity in the interaction potentials of the pressure and of the correlation functions and on the ergodicity of the equilibrium states in the gaseous phase. By similar methods we prove some cluster properties for the correlation functions in the gaseous phase.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ruelle, D.: Correlation functions of classical gases: Ann. Phys. (N. Y.)25, 109 (1963).
Penrose, O.: Convergence of fugacity expansions for fluids and lattice gases. J. Math. Phys.4, 1312 (1963).
Lebowitz, J. L., andO. Penrose: Convergence of virial expansions. J. Math. Phys.5, 841 (1964).
Ruelle, D.: Cluster property of correlation functions of classical gases. Rev. Mod. Phys.36, 580 (1964).
Ginibre, J.: Reduced density matrices of quantum gases I. Limit of infinite volume. J. Math. Phys.6, 238 (1965).
—— Reduced density matrices of quantum gases II. Cluster property. J. Math. Phys.6, 252 (1965).
Ruelle, D.: A variational formulation of equilibrium statistical mechanics. Commun. Math. Phys.5, 321 (1967).
Gallavotti, G., andS. Miracle-Sole: Statistical mechanics of lattice systems. Commun. Math. Phys.5, 317 (1967).
Dunford, N., andJ. Schwartz: Linear operators, vol. I. III.14 and VI.10.5. New York: Interscience 1958.
Hill, T. L.: Statistical mechanics. New York: McGraw-Hill 1956.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gallavotti, G., Miracle-Sole, S. Correlation functions of a lattice system. Commun.Math. Phys. 7, 274–288 (1968). https://doi.org/10.1007/BF01646661
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01646661