Nonequilibrium Phase Transition and Interfacial Properties in Driven Diffusive Systems.

It is well known that systems near critical points are very sensitive to external disturbances. This is because such systems are near the point of marginal stability. For disturbances of fixed sizes, the systems will exhibit critical properties different from those of the equilibrium ones as the correlation length exceeds the new length scale introduced by the disturbances. In other words, the systems belong to new universality classes. For systems of sufficiently large sizes and parameters close enough to critical points, this occurs even for small disturbances. This work presents an analytic study of one such situation which is probably the simplest example in this potentially rich field of nonequilibrium critical phenomena. The continuum model we studied corresponds to an Ising lattice-gas of charged particles driven by an external constant, uniform electric field E. The only locally conserved quantity is the scalar order parameter. We use a field theoretic renormalization group method to study its scaling properties near the critical point. A new fixed point stable below d_{c} = 5 is found to govern the critical behavior. Scaling forms of density correlation functions are derived and critical exponents are obtained to all orders in epsilon = 5 - d; thanks to a Ward identity resulted from a Galilean invariance of the kinetic equation. Spatial correlations are found to be very anisotropic with elongated correlations along the external field. Long wavelength fluctuations perpendicular to E are suppressed so effectively that the associated exponents are mean-field like. This calculation forms the first part of the thesis. The second part is a study of the low temperature interfacial properties of the above driven diffusive system. Starting from a bulk kinetic equation, an integral equation for the interface is derived. Nonlocal coupling between different parts of the interface arises from local particle conservation. The interface at any angle is shown to be stable against small deformation of all wavelength large compared to the interfacial width. However, the relaxation rate omega (k) for the interface exhibits a strong orientational dependence, which can be understood in terms of the modification of nonlocality by E. The wandering of the interface is then considered. Also, the possible stabilizing effect of periodic boundary condition on the orientation towards the direction of E is discussed.