Abstract
Analyticity and uniqueness of correlation functions is investigated for a number of systems by application of Ruelle's theorem on zeros of Asano contracted polynomials to the partition function. To answer the question when the partition function of a system is the Asano contraction of those of subsystems the groups appearing in the low and high temperature expansions are employed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Capocaccia, D., Cassandro, M., Ciccotti, G.: Equilibrium States of an Ising Ferromagnet in the Low Temperature Region. Preprint, Università di Roma
Gallavotti, G., Miracle-Sole, S.: Equilibrium States of the Ising Model in the Two-Phase Region, Phys. Rev. B5, 2555–2559 (1972)
Ginibre, J.: Cargèse Lectures, 1969, ed. by D. Kastler, New York: Gordon and Breach 1970
Kelly, D. G., Sherman, S.: General Griffiths Inequalities on Correlations in Ising Ferromagnets. J. Math. Phys.9, 466–484 (1968)
Lanford, O. E., Ruelle, D.: Observables at Infinity and States with Short Range Correlations in Statistical Mechanics, Commun. math. Phys.13, 194–215 (1969)
Merlini, D., Gruber, C.: Spin 1/2 Lattice Systems: Group Structure and Duality Relation J. Math. Phys.13, 1814–1823 (1972)
Messager, A., Trotin, J. C.: On Analyticity Properties of Pressure for Two-Body Ising Models. Preprint, Centre de Physique Théorique, Marseille 72/P. 496
Ruelle, D.: Statistical Mechanics. Rigorous Results. New York: Benjamin 1969
Ruelle, D.: Equilibrium Statistical Mechanics of Infinite Systems, in Les Houches Lectures, 1970. C. De Witt and R. Stora, eds., New York: Bordon and Breach
Ruelle, D.: On the Use of “Small External Field” in the Problem of Symmetry Breakdown in Statistical Mechanics, Ann. Phys. (N.Y.)69, 364–74 (1972)
Ruelle, D.: Extension of the Lee-Yang Circle Theorem, Phys. Rev. Letters26, 303–304 (1971)
Ruelle, D.: Some Remarks on the Location of Zeros of the Partition Function for Lattice Systems, Preprint
Slawny, J.: A Family of Equilibrium States Relevant to Low Temperature Behavior of Spin 1/2 Classical Ferromagnets. Breaking of Translation Symmetry. Preprint
Wegner, F. J.: Duality in Generalized Ising Models and Phase Transitions Without Local Parameters. J. Math. Phys.12, 2259–2272 (1971)
Griffiths, R. B.: Microcanonical Ensemble in Quantum Statistical Mechanics, J. Math. Phys.6, 1447–1461 (1965)
Wannier, G. H.: Antiferromagnetism. The Triangular Ising Net. Phys. Rev.79, 357–364 (1950)
Bourbaki, N.: Topologie Générale, Chap. VII, § 1, p. 75, Paris: Herman 1963
Dobrushin, R. L.: Gibbsian Random Fields for Lattice Systems with Pairwise Interactions. Funct. Anal. and Appl.2, 44–57 (1968)
Author information
Authors and Affiliations
Additional information
On leave of absence from Department of Physics and Astronomy, Tel Aviv University Ramat-Aviv, Israel.
Rights and permissions
About this article
Cite this article
Slawny, J. Analyticity and uniqueness for spin 1/2 classical ferromagnetic lattice systems at low temperatures. Commun.Math. Phys. 34, 271–296 (1973). https://doi.org/10.1007/BF01646474
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01646474