Calculation of the free energy of fullerenes in the Gross-Neveu model

Abstract

Methods of field theory on Riemannian manifolds were used to study the Gross–Neveu model (incorporating the Hubbard model as a special case) at T ≠ 0. The generating functional of the Gross–Neveu model on a torus, S2r ⊗ S1β, was obtained by the functional integration method. The model was regularized using the theory of zeta functions. Double sums were calculated using recurrent formulas. For the zeta function of the Dirac operator in the limit of s = 1, we obtained a polar singularity of the form 1/(s – 1), characteristic of the local limit of Green's function. The free energy density was computed as a function of the radius of the sphere r and inverse temperature β using the Maple 6 pack. The results show no anomalies, indicating that there are no phase transitions to the principal order in 1/N. However, taking into account the kink–antikink configurations of the scalar field A(x) in calculations without the 1/N expansion may drastically change the phase structure of the model.