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

Abstract

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

A model to study finite-size and magnetic effects on the phase transition of a fermion interacting system

“…In particular, the GN model shares some interesting features with QCD, like asymptotic freedom and dynamical symmetry breaking; moreover, it has a peculiar simplicity from the mathematical point of view. Extensions of this effective model have been made in many articles with applications to both condensed matter and hadronic physics [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Finite-size, chemical-potential and magnetic effects on the phase transition in a four-fermion interacting model

“…Among them, one of the simpler and most successful is the Gross-Neveu (GN) a e-mail: ecorrea@unifesspa.edu.br b e-mail: linharescesar@gmail.com c e-mail: adolfo@cbpf.br d e-mail: jmalboui@ufba.br e e-mail: asantana@unb.br model [3], considered as an effective theory for many situations in condensed-matter and in hadronic physics [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. It has proved to be an enlightening approach in describing properties of superconductors and graphene in condensed matter physics [5][6][7][8] and also phenomena in hadronic matter, such as spatial and thermal asymptotic freedom and the spatial and thermal confinement/deconfinement phase transition [13][14][15][16][17][18]. The GN model provides the simplest effective theory which may be considered as describing interactions between fermions, as a direct four-body coupling, where gauge fields and degrees of freedom are integrated out.…”

“…[16]; this has been done by an analysis of the four-point function at criticality, taking inspiration from linear response theory and the BCS theory of superconductivity [24]. We here approach the GN model in a non-standard way.…”

Finite-size effects on the phase transition in a four- and six-fermion interaction model

“…Compactification of spatial dimensions [5,6] is considered in a similar way. An unified treatment, generalizing various approaches dealing with finite-temperature and spatialcompactification concurrently, has been constructed [7,8,9] These methods have been employed to investigate spontaneous symmetrybreaking induced by temperature and/or spatial constraints in some bosonic and fermionic models describing phase transitions in condensed-matter, statistical and particle physics; for instance, for describing the size-dependence of the transition temperature of superconducting films, wires and grains [10,11]; for investigating size-effects in first-and second-order transitions [12,13,14,15]; and for analyzing size and magnetic-field effects on the Gross-Neveu (GN) [16] and the Nambu-Jona-Lasinio (NJL) [17] models, taken as effective theories [18] for hadronic physics [19,20,21].…”