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The behavior of the finite-temperature C-function, defined by Neto andFradkin [Nucl. Phys. B {\bf 400}, 525 (1993)], is analyzed within a d-dimensional exactly solvable lattice model, recently proposed by Vojta [Phys.Rev. B {\bf 53}, 710 (1996)], which is of the same universality class as thequantum nonlinear O(n) sigma model in the limit $n\to \infty$. The scalingfunctions of C for the cases d=1 (absence of long-range order), d=2 (existenceof a quantum critical point), d=4 (existence of a line of finite temperaturecritical points that ends up with a quantum critical point) are derived andanalyzed. The locations of regions where C is monotonically increasing (whichdepend significantly on d) are exactly determined. The results are interpretedwithin the finite-size scaling theory that has to be modified for d=4.  PACS number(s): 05.20.-y, 05.50.+q, 75.10.Hk, 75.10.Jm, 63.70.+h, 05.30-d,02.30Comment: 15 pages LATEX, ioplppt.sty file used, 6 EPS figures. Some changes  made in section V (on finite-size scaling interpretation of the results  obtained

On the finite-temperature generalization of theC-theorem and the interplay between classical and quantum fluctuations