Journal ArticleDOI
Phase transitions for φ{ 2 / 4 } quantum fields
TLDR
In this paper, phase transitions for the quantum field interaction λφ4+m02φ2,m02/λ≪1 were established in two dimensional space time.Abstract:
Phase transitions for the quantum field interaction λφ4+m02φ2,m02/λ≪1 are established in two dimensional space time.read more
Citations
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Journal ArticleDOI
Infrared Bounds, Phase Transitions and Continuous Symmetry Breaking
TL;DR: In this article, it was shown that phase transitions occur in (φ·φ) 3 2 quantum field theories and classical, isotropic Heisenberg models in 3 or more dimensions.
Journal ArticleDOI
Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions
TL;DR: The existence of spontaneous magnetization at sufficiently low temperature, and hence of a phase transition, in a variety of quantum spin systems in three or more dimensions was proved in this article.
Book
Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory
TL;DR: In this article, the authors used random walk representations as a tool to derive correlation inequalities for critical-exponent theory and the consequences of these inequalities for the theory of critical phenomena and quantum field theory.
Journal ArticleDOI
The random-walk representation of classical spin systems and correlation inequalities
TL;DR: In this article, a unified approach to many recently established correlation inequalities was presented, and a simple proof of the mass gap for the λ(φ4)2 quantum field model was obtained.
Journal ArticleDOI
Phase transitions and reflection positivity. I. General theory and long range lattice models
TL;DR: In this paper, the authors systematize the study of reflection positivity in statistical mechanical models, and thereby two techniques in the theory of phase transitions: the method of infrared bounds and the chessboard method of estimating contour probabilities in Peierls arguments.
References
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Journal ArticleDOI
Axioms for euclidean green's functions
TL;DR: In this paper, the necessary and sufficient conditions for Euclidean Green's functions to have analytic continuations to a relativistic field theory were given, extending and correcting a previous paper.
Journal ArticleDOI
The P(φ) 2 Euclidean Quantum Field Theory as Classical Statistical Mechanics
Journal ArticleDOI
The (φ4)2 Field Theory as a Classical Ising Model
Barry Simon,Robert B. Griffiths +1 more
TL;DR: In this article, an ensemble of spin 1/2 Ising spins with ferromagnetic pair interactions was used to prove a Lee-Yang theorem and GHS type correlation inequalities for the (φ4)2 theory.
Journal ArticleDOI
The λ(φ4)2 quantum field theory without cutoffsquantum field theory without cutoffs: III. The physical vacuum
James Glimm,Arthur Jaffe +1 more
Journal ArticleDOI
The λφ24 Quantum Field Theory without Cutoffs. IV. Perturbations of the Hamiltonian
James Glimm,Arthur Jaffe +1 more
TL;DR: In this paper, an inductive method to estimate the shift δE in the vacuum energy, caused by a perturbation δH of the P(φ)2 Hamiltonian H, is introduced.