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

• Published in: Physical review. D, Particles, fields, gravitation, and cosmology Particles, fields, gravitation, and cosmology, 2012-04, Vol.85 (8), Article 085015
• Main Authors: Khanna, F. C., Malbouisson, A. P. C., Malbouisson, J. M. C., Santana, A. E.
• Format: Article
• Language: English
• Subjects: Approximation; Asymptotic properties; Confining; Constants; Joining; Mathematical analysis; Mathematical models; Phase transformations; Topology
• ISSN: 1550-7998; 1550-2368
• DOI: 10.1103/PhysRevD.85.085015

(ProQuest: ... denotes formulae and/or non-USASCII text omitted) 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 ([lambda]), we find an asymptotic-freedom type of behavior, with g arrow right 0 as L arrow right 0 and/or T arrow right [infinity]. At T = 0, and for [lambda] [> or =] ... (the strong-coupling regime), we show that, starting in the region of asymptotic freedom and increasing L, a divergence of g appears at a finite value of L, signaling the existence of a phase transition with the system getting spatially confined. Such a spatial confinement is destroyed by raising the temperature. The confining length, ..., and the deconfining temperature, ..., are determined as functions of [lambda] and the mass (m) of the fermions, in the case of D = 2, 3, 4. Taking m as the constituent quark mass ([approximate] 350 MeV), the results obtained are of the same order of magnitude as the diameter ([approximate] 1.7 fm) and the estimated deconfining temperature ([approximate] 200 MeV) of hadrons.