## Abstract

To fix the notation, we consider the interaction with

$$V(\phi)=\lambda{\phi}^4+\sigma{\phi}^2-\mu\phi$$

(17.1.1)

*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 =*σ*_{c}, 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.)## Keywords

Ising Model Critical Exponent Scaling Limit Lattice Field Exponential Decay Rate
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## Copyright information

© Springer-Verlag New York Inc. 1987