The (2+1)-dimensional Gross–Neveu model with a U(1) chiral symmetry at nonzero temperature

Hands, Simon; Kogut, John B.; Strouthos, Costas

doi:10.1016/s0370-2693(01)00885-1

Cited by 40 publications

(43 citation statements)

References 34 publications

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“…In the 1 + 1 dimensional Gross-Neveu model the formation of Goldstone bosons is prohibited by the Coleman-MerminWagner theorem [42,43], which states the impossibility of spontaneously breaking a continuous global symmetry in 1 + 1 dimensions. A similar phenomenon has been observed in simulations of the 2+1d Gross-Neveu model at non-zero T [44]. While perhaps it not clear how to define the effective dimensionality of an anisotropic theory, we take from this analogy the notion that infra-red fluctuations remain important in the chirally symmetric phase; in other words the interaction between fermion and scalar degrees of freedom is strong.…”

Section: Discussionsupporting

confidence: 60%

Chiral symmetry restoration in anisotropicQED3

Thomas

Hands

2007

Phys. Rev. B

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We present results from a Monte Carlo simulation of non-compact lattice QED in 3 dimensions in which an explicit anisotropy κ between x and y hopping terms has been introduced into the action. Using a parameter set corresponding to broken chiral symmetry in the isotropic limit κ = 1, we study the chiral condensate on 16 3 , 20 3 , and 24 3 lattices as κ is varied, and fit the data to an equation of state which incorporates anisotropic volume corrections. The value κ c at which chiral symmetry is apparently restored is strongly volume-dependent, suggesting that the transition may be a crossover rather than a true phase transition. In addition we present results on 16 3 lattices for the scalar meson propagator, and for the Landau gauge-fixed fermion propagator. The scalar mass approaches the pion mass at large κ, consistent with chiral symmetry restoration, but the fermion remains massive at all values of κ studied, suggesting that strong infra-red fluctuations persist into the chirally symmetric regime. Implications for models of high-T c superconductivity based on anisotropic QED 3 are discussed.

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Section: Discussionsupporting

confidence: 60%

Chiral symmetry restoration in anisotropicQED3

Thomas

Hands

2007

Phys. Rev. B

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“…As before, the increase of the temperature destroys the spatial confinement that exists for λ ≥ λ (14) and (18) that…”

Section: B 3-d Compactified Gn Model At Finite Tmentioning

confidence: 65%

Phase transition in the massive Gross-Neveu model in toroidal topologies

Khanna

Malbouisson

et al. 2012

Phys. Rev. D

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We use methods of quantum field theory in toroidal topologies to study the N -component D-dimensional massive Gross-Neveu model, at zero and finite temperature, with compactified spatial coordinates. We discuss the behavior of the large-N coupling constant (g), investigating its dependence on the compactification length (L) and the temperature (T ). For all values of the fixed coupling constant (λ), we find an asymptotic-freedom type of behavior, with g → 0 as L → 0 and/or T → ∞. At T = 0, and for λ ≥ λ

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“…Using in the expression (9) a rather general formula ∞ −∞ dp 0 ln p 0 − A) = iπ|A| (10) (obtained rigorously, e.g., in Appendix B of [46] and true up to an infinite term independent on real quantity A), it is possible to reduce it to the following one:…”

Section: The Model and Its Thermodynamic Potentialmentioning

confidence: 99%

“…Partially, this interest is explained by more simple structure of QFT in two-, rather than in three spatial dimensions. As a result, it is much easier to investigate qualitatively such real physical phenomena as dynamical symmetry breaking [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and color superconductivity [15][16][17] as well as to model phase diagrams of real quantum chromodynamics [18,19] etc. in the framework of (2+1)-dimensional QFT.…”

Section: Introductionmentioning

confidence: 99%

Superconductivity Phenomenon Induced by External in-Plane Magnetic Field in (2 + 1)-Dimensional Gross–neveu Type Model

2013

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Phase structure of the (2+1)-dimensional model with four-fermion interaction of spin-1/2 quasiparticles (electrons) both in the fermion-antifermion (or chiral) and fermion-fermion (or superconducting) channels is considered at nonzero chemical potential µ and under the influence of an in-plane, i.e. parallel to a system sheet, external magnetic field B . It is shown that at sufficiently large values of µ and/or B the Cooper pairing (or superconducting) phase appears in the system at arbitrary relation between coupling constants, provided that there is an (arbitrary small) attractive interaction in the superconducting channel. In particular, at sufficiently weak attractive interaction in the chiral channel, the Cooper pairing occurs even at infinitesimal values of µ and/or B . The superconducting phase of the model is always a paramagnetic one.

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The (2+1)-dimensional Gross–Neveu model with a U(1) chiral symmetry at nonzero temperature

Cited by 40 publications

References 34 publications

Chiral symmetry restoration in anisotropicQED3

Chiral symmetry restoration in anisotropicQED3

Phase transition in the massive Gross-Neveu model in toroidal topologies

Superconductivity Phenomenon Induced by External in-Plane Magnetic Field in (2 + 1)-Dimensional Gross–neveu Type Model

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