Analyticity for one-dimensional systems with long-range superstable interactions
One-dimensional Gibbs systems
Springer Online Journal Archives 1860-2000
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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