One dimensional lattice gases with rapidly decreasing interaction

Archive for Rational Mechanics and Analysis - Tập 37 - Trang 181-191 - 1970
G. Gallavotti1, T. F. Lin1
1The Rockefeller University, New York City

Tóm tắt

We consider the pressure and the correlation functions of a one dimensional lattice gas in which the mutual interaction decreases as r exp-n t, (r, t>0), when the interparticle distance n→∞. We prove that such a system cannot show phase transitions of order k≧1 in the sense that the pressure and the correlation functions are infinitely differentiable with respect to any relevant parameter (such as the temperature or the chemical potential).

Tài liệu tham khảo

Mc Coy, B. M., Private communication. Ruelle, D., Comm. Math. Phys. 9, 267 (1968). Gallavotti, G., S. Miracle-Sole, & D. Ruelle, Phys. Lett. 26A, 350 (1968). Gallavotti, G., & S. Miracle-Sole, J. Math. Phys. 11, 147 (1970). Fisher, M. E., Arch. Rational Mech. Anal. 17, 377 (1964). See also [9]. Fisher, M. E., Physics 3, 255 (1967). Dyson, F. J., Comm. Math. Phys. 12, 91 (1969). Dyson, F. J., Non-Existence of Spontaneous Magnetization in a One-Dimensional Ising Ferromagnet. Institute for Advanced Study, Princeton, N.J., preprint. See for instance M. E. Fisher: J. Math. Phys. 6, 1643 (1965). See also G. Gallavotti, & S. Miracle-Sole: Comm. Math. Phys. 5, 317 (1967).