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We report some selected recent developments in the finite-size scaling theory of critical phenomena occurring in systems with strong spatial anisotropies. Such systems are characterized by correlation lengths divergent with different exponents (ν_⊥, ν_||) along different directions. Attention is focused on the driven diffusive lattice gas that exhibits a second order nonequilibrium phase transition. We present in detail the phenomenology and its comparison with computer simulation. Novel features of finite-size effects in anisotropic nonequilibrium systems are emphasized.

We study the standard three-dimensional driven diffusive system on a simple cubic lattice where particle jumping along a given lattice direction are biased by an infinitely strong field, while those along other directions follow the usual Kawasaki dynamics. Our goal is to determine which of the several existing theories for critical behavior is valid. We analyze finite-size scaling properties using a range of system shapes and sizes far exceeding previous studies. Four different analytic predictions are tested against the numerical data. Binder and Wang's prediction does not fit the data well. Among the two slightly different versions of Leung, the one including the effects of a dangerous irrelevant variable appears to be better. Recently proposed isotropic finite-size scaling is inconsistent with our data from cubic systems, where systematic deviations are found, especially in scaling at the critical temperature.

We investigate the effect of hydrodynamic interactions on the non-equilibrium dynamics of an ideal flexible polymer pulled by a constant force applied at one polymer end using the perturbation theory. For moderate force, if the polymer elongation is small, the hydrodynamic interactions are not screened and the velocity and the longitudinal elongation of the polymer are computed using the renormalization group method. For large chain lengths and a finite force the hydrodynamic interactions are only partially screened, which in three dimensions results in unusual logarithmic corrections to the velocity and the longitudinal elongation.