Theoretical research will be conducted in two areas: phase transitions and noneqilibrium interfaces. A new method of analyzing simulation data will be used, including finite size scaling of distributions of energy and order parameter. This can detect weakly first order transitions and accurately estimate exponents. Extensions to systems with continuous symmetries, frustrated junction arrays and random systems will be made. Two- dimensional XY-like transitions will be studied to see if unambiguous numerical detection is feasible. Two aspects of driven interfaces will be studied by analytical and numerical methods. The first study is of the rough-smooth transition in dimensions greater than three and molecular beam epitaxy growth focussing on effects of initial conditions and the connections between logarithmic and algebraic roughness in vicinal surfaces. The second study is of directional solidification and eutectic growth driven by a moving temperature gradient by full phase, rather than interface, models. Successful simulations in one- and two-dimension interfaces have been done. Extensions to allow for thermal and external noise, a study of interface instabilities, and comparison to experiments will be made. Generalizations to include convective effects and to interpolations between one- and two-sided models will be made. %%% The theoretical research focuses on two areas of broad interest and importance in condensed matter physics and materials science. Sophisticated numerical techniques developed by the principal investigator will be exploited to determine the nature of the phase transition in a variety of complex systems. The results will have profound impact on the study of phase transitions and critical phenomena. In addition, the results will provide a better understanding of the real materials systems involved. A second area of study will be the growth of interfaces. This area is one of fascinating fundamental interest, yet also has important ramifications for materials processing through crystal growth and thin film growth.
