Fourfermi theories in fewer than four dimensions
Abstract
Fourfermi 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 nontrivially 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 secondorder 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 nonzero temperature, and the scalar twopoint correlation function in the vicinity of the bulk transition. All of the results are in excellent agreement with analytic predictions andmore »
 Authors:

 Univ. of Glasgow (United Kingdom) CERN, Geneva (Switzerland)
 CERN, Geneva (Switzerland)
 Univ. of Illinois, UrbanaChampaign (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 00034916
 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. Fourfermi 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. Fourfermi theories in fewer than four dimensions. United States. doi:10.1006/aphy.1993.1039.
Hands, S, Kocic, A, and Kogut, J B. Sat .
"Fourfermi theories in fewer than four dimensions". United States. doi:10.1006/aphy.1993.1039.
@article{osti_6217183,
title = {Fourfermi theories in fewer than four dimensions},
author = {Hands, S and Kocic, A and Kogut, J B},
abstractNote = {Fourfermi 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 nontrivially 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 secondorder 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 nonzero temperature, and the scalar twopoint 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 = {00034916},
number = ,
volume = 224:1,
place = {United States},
year = {1993},
month = {5}
}