Abstract
Phase transitions were studied in the 3D Gross–Neveu model on a sphere at T ≠ 0. The zeta function of the Dirac operator of the model was represented with a double sum, and its derivative was calculated using recurrent formulas for generalized Epstein–Hurwitz functions. The effective potential Vwas determined as a function of the σ field, temperature T, and inverse radius of curvature r. Phase transitions first-order in temperature at R= 0 (T c = 1/2 ln 2) and second-order in curvature R= 2/r 2 at T= 0 (r c = 1/1.5) were identified. For the general case, T ≠ 0 and R ≠ 0, the critical phase dependence T c(r c) was obtained, and the V(σ, T, r) surface was constructed. External stimuli such as temperature and curvature were shown to restore the symmetry of the system in the 3DGross–Neveu model.
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Kalinkin, A.N., Skorikov, V.M. Phase Transitions in the Gross–Neveu Model on a Sphere for High-T c Materials. Inorganic Materials 38, 1148–1152 (2002). https://doi.org/10.1023/A:1020970600940
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DOI: https://doi.org/10.1023/A:1020970600940