Phase transition in the 3D massive Gross-Neveu model

¹ Department of Physics, Theoretical Physics Institute, University of Alberta - Edmonton, Alberta, T6G 2J1, Canada
² TRIUMF - 4004, Westbrook mall, Vancouver, British Columbia V6T 2A3, Canada
³ Centro Brasileiro de Pesquisas Físicas, MCT - 22290-180, Rio de Janeiro, RJ, Brazil
⁴ Instituto de Física, Universidade Federal da Bahia - 40210-340, Salvador, BA, Brazil
⁵ Instituto de Física, International Center for Condensed Matter Physics, Universidade de Brasília 70910-900, Brasilia, DF, Brazil

^a adolfo@cbpf.br

Received: 24 August 2010
Accepted: 22 September 2010

Abstract

We consider the 3-dimensional massive Gross-Neveu model at finite temperature as an effective theory for strong interactions. Using the Matsubara imaginary-time formalism, we derive a closed form for the renormalized T-dependent four-point function. This gives a singularity, suggesting a phase transition. Considering the free energy we obtain the T-dependent mass, which goes to zero for some temperature. These results lead us to the conclusion that there is a second-order phase transition.