Abstract
Abstract The Nambu–Jona-Lasinio (NJL) model is one of the most frequently used four-fermion models in the study of dynamical symmetry breaking. In particular, the NJL model is convenient for that analysis at finite temperature, chemical potential and size effects, as has been explored in the last decade. With this motivation, we investigate the finite-size effects on the phase structure of the NJL model in D = 3 Euclidean dimensions, in the situations that one, two and three dimensions are compactified. In this context, we employ the zeta-function and compactification methods to calculate the effective potential and gap equation. The critical lines that separate trivial and non-trivial fermion mass phases in a second order transition are obtained. We also analyze the system at finite temperature, considering the inverse of temperature as the size of one of the compactified dimensions.
Highlights
The last decades witnessed significant investigations on the phase structure of quantum field theories, in particular on the chiral symmetry phase transitions in Quantum Cromodynamics (QCD)
The NJL model is specially convenient for the investigation of dynamical symmetries when the system is under certain conditions, like finite temperature, finite chemical potential, external gauge field, gravitation field and others [2, 3, 4]
Ref. [6] performed a numerical investigation of a three-dimensional four-fermion model in a finite-size scaling analysis, where the finite-size effects act as an external field
Summary
The last decades witnessed significant investigations on the phase structure of quantum field theories, in particular on the chiral symmetry phase transitions in Quantum Cromodynamics (QCD). Finite-size effects on the phase transitions of four-fermion models have attracted a great interest [5, 6, 7]. We study the Euclidean three-dimensional NJL model in the framework of zeta-function and compactification methods [9] This procedure in principle allows us to explore the mentioned model with one, two or three compactified dimensions with antiperiodic boundary conditions [17] and compare their effects in the phase diagram of the model. We associate one of the compactified coordinates to the range [0, β], where β is the inverse of the temperature T In this setting, we calculate and determine analytically the size-dependence of the effective potential and gap equation.
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