Finite-size effects on the phase transition in the three-dimensional Gross-Neveu model

¹ Department of Physics, Theoretical Physics Institute, University of Alberta - Edmonton, Alberta, T6G 2J1, Canada
² TRIUMF - 4004, Wesbrook 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 Departamento de Física, Faculdade de Ciências, Universidade do Porto - 4169-007, Porto, Portugal
⁶ Instituto de Física, International Centre for Condensed Matter Physics, Universidade de Brasília 70.910-900, Brasília, DF, Brazil

^a fkhanna@ualberta.ca
^b adolfo@cbpf.br
^c jmalboui@ufba.br
^d asantana@unb.br

Received: 27 September 2011
Accepted: 28 November 2011

Abstract

We discuss finite-size effects on the phase transition in the two-component, massive, three-dimensional Gross-Neveu model. From an analysis of four-point function and from the existence of a stable infrared fixed point of the beta-function, we get indications of the existence of a second-order phase transition. Using a generalized Matsubara prescription and zeta-function regularization techniques, we determine the dependence of the critical temperature on the size of the system.