Critical and Tricritical Points for the Massless 2d Gross-Neveu Model Beyond Large N

Abstract

Using optimized perturbation theory, we evaluate the effective potential for the massless two dimensional Gross-Neveu model at finite temperature and density containing corrections beyond the leading large-N contribution. For large-N, our results exactly reproduce the well known 1/N leading order results for the critical temperature, chemical potential and tricritical points. For finite N, our critical values are smaller than the ones predicted by the large-N approximation and seem to observe Landau's theorem for phase transitions in one space dimension. New analytical results are presented for the tricritical points that include 1/N corrections. The easiness with which the calculations and renormalization are carried out allied to the seemingly convergent optimized results displayed, in this particular application, show the robustness of this method and allows us to obtain neat analytical expressions for the critical as well as tricritical values beyond the results currently known.

29 pages, 14 figures

References in corpus (2)

• Asymptotically Improved Convergence of Optimized Perturbation Theory in the Bose-Einstein Condensation Problem
• Non-universal Critical Quantities from Variational Perturbation Theory and Their Application to the BEC Temperature Shift

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• Nonperturbative Yukawa theory at finite density and temperature
• Perturbative Yukawa theory at finite density: the role of masses and renormalization group flow at two loops
• An extension of the Linear Delta Expansion to Superspace
• Phase diagram of quark-antiquark and diquark condensates in the 3-dimensional Gross Neveu model with the 4-component spinor representation