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The φ4 Critical Point

  • James Glimm
  • Arthur Jaffe

Abstract

To fix the notation, we consider the interaction
$$V(\phi)=\lambda{\phi}^4+\sigma{\phi}^2-\mu\phi$$
(17.1.1)
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.)

Keywords

Ising Model Critical Exponent Scaling Limit Lattice Field Exponential Decay Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • James Glimm
    • 1
  • Arthur Jaffe
    • 2
  1. 1.Courant Institute for Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Harvard UniversityCambridgeUSA

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