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Nonlinear current-voltage characteristics have been measured for ultrathin (16–400 A) YBa2Cu3O7−δ films in high magnetic fields. A scaling analysis of these data reveals deviations from the universal vortex-glass critical scaling behavior observed for thick films. This is argued to be a dimensionality effect: At large currents, one probes length scales smaller than the film thickness, i.e., the three-dimensional (3d) vortex-glass behavior, whereas at low currents the vortex excitations involve typical length scales which exceed the film thickness, hence the 2d behavior is exhibited. Further evidence for this picture is found from the 3d vortex-glass correlation length, which appears to be cut off by the film thickness.

The procedure of Bulaevskiǐ, Ledvij, and Kogan for evaluating the line energy of a single, straight vortex in the Lawrence-Doniach model in the linearized phase-only approximation is modified to take accurate account of the vortex core cross-sections. Dimensional crossover effects are found to be pronounced, with oscillations in the angular dependence of the torque for θ ⋍ π/2 and T ≈ T ∗ c .

Bose-Einstein condensation in an ideal quasi-two-dimensional Bose gas is reconsidered with a view of establishing a simple criterion for crossover effects from two- to three-dimensional systems. The main attention is focused on the density of states involved. It is deduced that the critical value at which these effects occur is universal, apart from a geometrical factor of the order of unity. The implications for strongly interacting Bose systems are discussed very briefly.

The crossover effect of dimensionality in a disordered layered system has been studied by using the Beyond-CPA method for the vertex. The effective dimensions of the system are determined by the interlayer coupling t . It is shown that the Anderson transition occurs at the critical value t c . The dynamical conductivity, the d.c. conductivity and the localization length near the critical point have been calculated analytically.