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Title: Four-fermi theories in fewer than four dimensions

Abstract

Four-fermi models in dimensionality 2 < d < 4 exhibit an ultraviolet stable renormalization group fixed point at a strong value of the coupling constant where chiral symmetry is spontaneously broken. The resulting field theory describes relativistic fermions interacting non-trivially via exchange of scalar bound states. The authors calculate the O(1/N[sub f]) corrections to this picture, where N[sub f] is the number of fermion species, for a variety of models and confirm their renormalizability to this order. A connection between renormalizability and the hyperscaling relations between the theory's critical exponents is made explicit. Results are presented of extensive numerical simulations of the simplest model for d = 3, performed using the hybrid Monte Carlo algorithm on lattice sizes ranging from 8[sup 3] to 24[sup 3]. For N[sub f] = 12 species of massless fermions the existence is confirmed of a second-order phase transition where chiral symmetry is spontaneously broken. Using both direct measurement and finite size scaling arguments the critical exponenets [beta],[gamma],[nu], and [delta] are estimated. The authors also investigate symmetry, restoration at non-zero temperature, and the scalar two-point correlation function in the vicinity of the bulk transition. All of the results are in excellent agreement with analytic predictions andmore » support the contention that the 1/N[sub f], expansion is accurate for this class of model. 37 refs., 18 figs., 14 tabs.« less

Authors:
 [1];  [2];  [3]
  1. Univ. of Glasgow (United Kingdom) CERN, Geneva (Switzerland)
  2. CERN, Geneva (Switzerland)
  3. Univ. of Illinois, Urbana-Champaign (United States)
Publication Date:
OSTI Identifier:
6217183
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York); (United States)
Additional Journal Information:
Journal Volume: 224:1; Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Pa; CHIRAL SYMMETRY; SYMMETRY BREAKING; FERMI INTERACTIONS; FIELD THEORIES; RENORMALIZATION; STATISTICAL MECHANICS; VACUUM STATES; BASIC INTERACTIONS; INTERACTIONS; MECHANICS; SYMMETRY; WEAK INTERACTIONS; 662200* - Specific Theories & Interaction Models; Particle Systematics- (1992-); 662120 - General Theory of Particles & Fields- Symmetry, Conservation Laws, Currents & Their Properties- (1992-); 662110 - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)

Citation Formats

Hands, S, Kocic, A, and Kogut, J B. Four-fermi theories in fewer than four dimensions. United States: N. p., 1993. Web. doi:10.1006/aphy.1993.1039.
Hands, S, Kocic, A, & Kogut, J B. Four-fermi theories in fewer than four dimensions. United States. doi:10.1006/aphy.1993.1039.
Hands, S, Kocic, A, and Kogut, J B. Sat . "Four-fermi theories in fewer than four dimensions". United States. doi:10.1006/aphy.1993.1039.
@article{osti_6217183,
title = {Four-fermi theories in fewer than four dimensions},
author = {Hands, S and Kocic, A and Kogut, J B},
abstractNote = {Four-fermi models in dimensionality 2 < d < 4 exhibit an ultraviolet stable renormalization group fixed point at a strong value of the coupling constant where chiral symmetry is spontaneously broken. The resulting field theory describes relativistic fermions interacting non-trivially via exchange of scalar bound states. The authors calculate the O(1/N[sub f]) corrections to this picture, where N[sub f] is the number of fermion species, for a variety of models and confirm their renormalizability to this order. A connection between renormalizability and the hyperscaling relations between the theory's critical exponents is made explicit. Results are presented of extensive numerical simulations of the simplest model for d = 3, performed using the hybrid Monte Carlo algorithm on lattice sizes ranging from 8[sup 3] to 24[sup 3]. For N[sub f] = 12 species of massless fermions the existence is confirmed of a second-order phase transition where chiral symmetry is spontaneously broken. Using both direct measurement and finite size scaling arguments the critical exponenets [beta],[gamma],[nu], and [delta] are estimated. The authors also investigate symmetry, restoration at non-zero temperature, and the scalar two-point correlation function in the vicinity of the bulk transition. All of the results are in excellent agreement with analytic predictions and support the contention that the 1/N[sub f], expansion is accurate for this class of model. 37 refs., 18 figs., 14 tabs.},
doi = {10.1006/aphy.1993.1039},
journal = {Annals of Physics (New York); (United States)},
issn = {0003-4916},
number = ,
volume = 224:1,
place = {United States},
year = {1993},
month = {5}
}