Published 1976 | Version v1
Journal article Metadata-only

Infrared bounds, phase transitions and continuous symmetry breaking

Creators

  • 1. Princeton Univ., N.J. (USA). Dept. of Mathematics
  • 2. Rockefeller Univ., New York (USA). Dept. of Mathematics

Description

We present a new method for rigorously proving the existence of phase transitions. In particular, we prove that phase transitions occur in (PHI*PHI)2 quantum field theories and classical, isotopic Heisenberg models in 3 or more dimensions. The central element of the proof is that for fixed ferromagnetic nearest neighbor coupling, the absolutely continuous part of the two point function in k space is bounded by O(k-2). When applicable, our results can be fairly accurate numerically. (orig.)

Abstract (German)

Es wird eine neue Methode fuer den strengen Beweis der Existenz von Phasenuebergaengen vorgelegt. Insbesondere wird bewiesen, dass Phasenuebergaenge in (PHI*PHI)2 Quantenfeldtheorien und im klassischen, isotropen Heisenbergmodell in drei oder mehr Dimensionen auftreten. Der zentrale Punkt des Beweises ist, dass fuer feste, ferromagnetische Kopplung naechster Nachbarn, der absolut kontinuierliche Teil der Zweipunktfunktion im k-Raum durch O(k-2) begrenzt ist. Die Ergebnisse lassen fuer Anwendungsfaelle hinreichend genau berechnen. (orig.)

Additional details

Identifiers

DOI
10.1007/bf01608557;

Publishing Information

Journal Title
Communications in Mathematical Physics
Journal Volume
50
Journal Issue
1
Series
Commun. Math. Phys.
Journal Page Range
79-95
ISSN
0010-3616

INIS

Country of Publication
Germany
Country of Input or Organization
Germany
INIS RN
8302106
Subject category
S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
Descriptors DEI
CRITICAL TEMPERATURE; FERROMAGNETISM; HEISENBERG MODEL; ISING MODEL; ORDER-DISORDER TRANSFORMATIONS; QUANTUM FIELD THEORY; SYMMETRY BREAKING
Descriptors DEC
CRYSTAL MODELS; FIELD THEORIES; MAGNETISM; MATHEMATICAL MODELS; PHASE TRANSFORMATIONS; PHYSICAL PROPERTIES; THERMODYNAMIC PROPERTIES; TRANSITION TEMPERATURE

Optional Information

Notes
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