On the finite-size behavior of systems with asymptotically large critical shift

Exact results of the finite-size behavior of the susceptibility in three-dimensional mean spherical model films under Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The corresponding scaling functions are explicitly derived and their asymptotics close to, above and below the bulk critical temperature $T_c$ are obtained. The results can be incorporated in the framework of the finite-size scaling theory where the exponent $\lambda$ characterizing the shift of the finite-size critical temperature with respect to $T_c$ is smaller than $1/\nu$, with $\nu$ being the critical exponent of the bulk correlation length.Comment: 24 pages, late

Out-of-equilibrium properties of the semi-infinite kinetic spherical model

We study the ageing properties of the semi-infinite kinetic spherical model at the critical point and in the ordered low-temperature phase, both for Dirichlet and Neumann boundary conditions. The surface fluctuation-dissipation ratio and the scaling functions of two-time surface correlation and response functions are determined explicitly in the dynamical scaling regime. In the low-temperature phase our results show that for the case of Dirichlet boundary conditions the value of the non-equilibrium surface exponent $b_1$ differs from the usual bulk value of systems undergoing phase ordering.Comment: 22 pages, 4 figures included, submitted to J. Phys.

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 {\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 the quantum nonlinear O(n) sigma model in the limit $n\to \infty$. 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 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