Abstract
We systematize the study of reflection positivity in statistical mechanical models, and thereby two techniques in the theory of phase transitions: the method of infrared bounds and the chessboard method of estimating contour probabilities in Peierls arguments. We illustrate the ideas by applying them to models with long range interactions in one and two dimensions. Additional applications are discussed in a second paper.
Research partially supported by US National Science Foundation under Grant MPS-75-11864
Research partially supported by Canadian National Research Council under Grant A4015
Research partially supported by US National Science Foundation under Grant MCS-75-21684A01
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Fröhlich, J., Israel, R., Lieb, E.H., Simon, B. (1978). Phase Transitions and Reflection Positivity. I. General Theory and Long Range Lattice Models. In: Nachtergaele, B., Solovej, J.P., Yngvason, J. (eds) Statistical Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10018-9_13
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DOI: https://doi.org/10.1007/978-3-662-10018-9_13
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