On the Finite–Temperature Generalization of the C-theorem and the Interplay between Classical and Quantum Fluctuations

The behavior of the finite-temperature C-function, defined by Neto and Fradkin [Nucl. Phys. B 400, 525 (1993)], is analyzed within a d-dimensional exactly solvable lattice model, recently proposed by Vojta [Phys. Rev. B 53, 710 (1996)], which is of the same universality class as the quantum nonlinear O(n) sigma model in the limit n → ∞. The scaling functions of C for the cases d = 1 (absence of long-range order), d = 2 (existence of a quantum critical point), d = 4 (existence of a line of finite temperature critical points that ends up with a quantum critical point) are derived and analyzed. The locations of regions where C is monotonically increasing (which depend significantly on d) are exactly determined. The results are interpreted within the finite-size scaling theory that has to be modified for d = 4. PACS numbers: 05.20.-y, 05.50.+q, 75.10.Hk, 75.10.Jm, 63.70.+h, 05.30-d, 02.30 Short title: On the Generalization of the C-theorem