To fix the notation, we consider the interaction
with λ, σ, and µ real and 0 < λ. By the Lee-Yang theorem, there is no phase transition for µ ≠ 0. The high temperature series expansions (Chapter 18) show that there is no phase transition for µ = 0 and σ sufficiently large. By Section 16.2, there is a phase transition for µ = 0 and σ sufficiently negative. In the latter region one expects exactly two phases, and a unique value of σ, σ = σc, which separates the one and two phase regions. Throughout this chapter we define σ c as the infinum of the values of σ for which (17.1.1) has a unique phase and exponential decay of correlations. (Thus H has a gap in its spectrum, which separates 0, the spectrum of the vacuum Ω, from the rest of the spectrum. We call this gap a mass m> 0.)
KeywordsIsing Model Critical Exponent Scaling Limit Lattice Field Exponential Decay Rate
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© Springer-Verlag New York Inc. 1987