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Title: From nondegenerate conducting polymers to dense matter in the massive Gross-Neveu model

Abstract

Using results from the theory of nondegenerate conducting polymers like cis-polyacetylene, we generalize our previous work on dense baryonic matter and the soliton crystal in the massless Gross-Neveu model to finite bare fermion mass. In the large N limit, the exact crystal ground state can be constructed analytically, in close analogy to the bipolaron lattice in polymers. These findings are contrasted to the standard scenario with homogeneous phases only and a first order phase transition at a critical chemical potential.

Authors:
;  [1]
  1. Institut fuer Theoretische Physik III, Universitaet Erlangen-Nuernberg, D-91058 Erlangen (Germany)
Publication Date:
OSTI Identifier:
20711587
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.72.105008; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BARYONS; CRYSTALS; GROUND STATES; PHASE TRANSFORMATIONS; POLYMERS; POTENTIALS; REST MASS; SOLITONS

Citation Formats

Thies, Michael, and Urlichs, Konrad. From nondegenerate conducting polymers to dense matter in the massive Gross-Neveu model. United States: N. p., 2005. Web. doi:10.1103/PhysRevD.72.105008.
Thies, Michael, & Urlichs, Konrad. From nondegenerate conducting polymers to dense matter in the massive Gross-Neveu model. United States. doi:10.1103/PhysRevD.72.105008.
Thies, Michael, and Urlichs, Konrad. Tue . "From nondegenerate conducting polymers to dense matter in the massive Gross-Neveu model". United States. doi:10.1103/PhysRevD.72.105008.
@article{osti_20711587,
title = {From nondegenerate conducting polymers to dense matter in the massive Gross-Neveu model},
author = {Thies, Michael and Urlichs, Konrad},
abstractNote = {Using results from the theory of nondegenerate conducting polymers like cis-polyacetylene, we generalize our previous work on dense baryonic matter and the soliton crystal in the massless Gross-Neveu model to finite bare fermion mass. In the large N limit, the exact crystal ground state can be constructed analytically, in close analogy to the bipolaron lattice in polymers. These findings are contrasted to the standard scenario with homogeneous phases only and a first order phase transition at a critical chemical potential.},
doi = {10.1103/PhysRevD.72.105008},
journal = {Physical Review. D, Particles Fields},
number = 10,
volume = 72,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}
  • The phase diagram of the massive chiral Gross-Neveu model (the massive Nambu-Jona-Lasinio model in 1+1 dimensions) is constructed. In the large N limit, the Hartree-Fock approach can be used. We find numerically a chiral crystal phase separated from a massive Fermi gas phase by a 1st order transition. Using perturbation theory, we also construct the critical sheet where the homogeneous phase becomes unstable in a 2nd order transition. A tricritical curve is located. The phase diagram is mapped out as a function of fermion mass, chemical potential and temperature, and compared with the one of the discrete chiral Gross-Neveu model.more » As a by-product, we illustrate the crystal structure of matter at zero temperature for various densities and fermion masses.« less
  • We consider the massive Euclidean Gross-Neveu model. Thanks to the Pauli principle the bare perturbation expansion for the model with an ultraviolet cutoff is convergent in a disk whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant. The theory constructed in this way is physical (it satisfies Osterwalder and Schrader's axioms) in contrast with the planar theories obtained by similar perturbative expansions.
  • We study the thermodynamics of massive Gross-Neveu models with explicitly broken discrete or continuous chiral symmetries for finite temperature and fermion densities. The large [ital N] limit is discussed, paying attention to the no-go theorems for symmetry breaking in two dimensions which apply to the massless cases. The main purpose of the study is to serve as an analytical orientation for the more complex problem of the chiral transition in four-dimensional QCD with quarks. For any nonvanishing fermion mass, we find, at finite densities, lines of first-order phase transitions. For small mass values, traces of would-be second-order transitions and amore » tricritical point are recognizable. We study the thermodynamics of these models, and in the model with broken continuous chiral symmetry we examine the properties of the pionlike state.« less
  • We perform a 1/N expansion of the partition function of the massive Gross-Neveu model in 1+1 dimensions. The procedure allows for the inclusion of the contribution of scalar and pseudoscalar composites (of order 1/N) to the equation of state. The naive expectation that the bosonic fluctuations significantly correct the mean field approximation at low temperatures is confirmed by our calculations. Actually the relevant degrees of freedom of hadronic matter at low temperatures are found to be pionlike excitations, rather than the fundamental constituents. {copyright} {ital 1997} {ital The American Physical Society}
  • The massive Gross-Neveu model is treated self-consistently in the leading order of the 1/N expansion. The properties of the model when the temperature and the chemical potential are included are studied. It is shown that there exists a critical value of the chemical potential at which the effective mass of the fermion abruptly changes its value.