Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Physics and Astronomy

First Advisor

Dana Browne


It is well established that anisotropy does not affect the critical behavior of a system in thermodynamic equilibrium undergoing a second order phase transition. We study here an anisotropic kinetic model for heterogeneous catalysis which mimics the oxidation of CO on the (110) surface of a transition metal like Pd. In this model, the oxidation process occurs at an infinite reaction rate. We mapped out the phase diagram of possible steady states for various anisotropic reaction and absorption processes as a function of the O$\sb2$/CO adsorption rate and the CO diffusion rate. The phase diagram depends upon the amount of anisotropy and exhibits both a first order and a second order phase transition. We also examined the critical behavior at the second order phase transition with finite size scaling and found that this model belongs to the directed percolation universality class irrespective of the anisotropy. Furthermore, we extended this model to include finite reaction rates. We found evidence of a new feature here, namely a tricritical point. We have developed a theory to account for this new feature. The critical behavior of this modified model belongs to the same universality class as the original model except at the tricritical point. To better understand the physics of nonequilibrium transitions, we studied the behavior of various dynamic modes utilizing the master equation and finite size scaling. This master equation approach indicated that dynamic phase transition is a consequence of the emergence of new steady states. This approach affords a connection with the traditional method of transfer matrix.