Abstract
We consider unbounded spin systems and classical continuous particle systems in one dimension. We assume that the interaction is described by a superstable two-body potential with a decay at large distances at least asr −2(lnr)−(2+ε), ε > 0. We prove the analyticity of the free energy and of the correlations as functions of the interaction parameters. This is done by using a “renormalization group technique” to transform the original model into another, physically equivalent, model which is in the high-temperature (small-coupling) region.
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G.N.A.F.A.-C.N.R.
G.N.S.M.-C.N.R.
G.N.F.M.-C.N.R.
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Campanino, M., Capocaccia, D. & Olivieri, E. Analyticity for one-dimensional systems with long-range superstable interactions. J Stat Phys 33, 437–476 (1983). https://doi.org/10.1007/BF01009805
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DOI: https://doi.org/10.1007/BF01009805