Finite-size effects on the phase diagram of difermion condensates in two-dimensional four-fermion interaction models

Abstract

We investigate finite-size effects on the phase structure of chiral and difermion condensates at finite temperature and density in the framework of the two-dimensional large-N Nambu-Jona-Lasinio model. We take into account size-dependent effects by making use of zeta-function and compactification methods. The thermodynamic potential and the gap equations for the chiral and difermion condensed phases are then derived in the mean-field approximation. Size-dependent critical lines separating the different phases are obtained considering antiperiodic boundary conditions for the spatial coordinate.

Integrable Gross-Neveu models with fermion-fermion and fermion-antifermion pairing

“…This enabled us to generate a new integrable model by applying the duality transformation (ψ 1 → ψ Eq. (10). We now try to construct another integrable model by "self-dualizing" the GN Lagrangian.…”

“…We now try to construct another integrable model by "self-dualizing" the GN Lagrangian. This means that we add the interaction term of the dual GN model (10) to the GN model Lagrangian (9), so that the full Lagrangian shares the discrete part of the Pauli-Gürsey symmetry with the free, massless theory,…”

“…Other four-fermion interactions which can be found in the literature interpolate between (1) and (2) by introducing two different coupling constants [3][4][5], or have extra terms which give rise to fermion-fermion pairing rather than fermion-antifermion pairing [6][7][8][9][10][11][12]. The motivation for the latter models comes mostly from the predicted phenomenon of color superconductivity in quantum chromodynamics [13][14][15].…”

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].…”

Quark deconfinement phase transition in nuclear matter for improved quark mass density-dependent model

“…many theoretical efforts have been recently and less recently carried out, on the study of the hadronic phase structure and the deconfinement phase transition by using the Nambu-Jona-Lasinio model and some its extensions in the framework of finite temperature field theory [19][20][21][22][23][24][25][26][27][28][29][30]. Among them, some perform a very detailed investigation of the QCD phase structure and other ones give precise numerical estimates for the deconfinement temperature and size of hadrons.…”