Abstract
The method of infrared bounds is extended to a large class of nearest neighbour interactions in classical spin systems. Temperature controlled bounds on fluctuations follow whenever the coupling function is a positive definite kernel. Existence of phase transitions is demonstrated for the RP Nmodel for d≥3.
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References
Berg, C., Christensen, J. P. R., and Ressel, P., Harmonic Analysis on Semigroups, Springer, New York, 1984.
Dyson, F., Lieb, E. H., and Simon, B., Phase transitions in quantum spin systems with isotropic and nonisotropic interactions, J. Stat. Phys. 18, 335 (1978).
Fröhlich, J., Simon, B., and Spencer, T., Infrared bounds, phase transitions, and continuous symmetry breaking, Commun. Math. Phys. 50, 79 (1976).
Fröhlich, J., Israel, R., Lieb, E. H., and Simon, B., Phase transitions and reflection positivity. I, Commun. Math. Phys. 62, 1 (1978).
Fröhlich, J. Israel, R., Lieb, E. H., and Simon, B., Phase transitions and reflection positivity. II, J. Stat. Phys. 22, 297 (1980).
Glimm, J. and Jaffe, A., Quantum Physics, 2nd edn., Springer, New York, 1987.
Rudin, W., Functional Analysis, McGraw-Hill, NY, 1973.
Ruelle, D., Statistical Mechanics, Benjamin, London, 1969.