My research interests involve theoretical studies in condensed matter physics. I am interested in cooperative phenomena in systems with competing interactions and disorder. A brief summary of some of these topics is given below.

Investigations of the effects of disorder on both static critical phenomena in magnets and the dynamical properties of solids are being carried out. Disorder can arise in many ways such as the dilution of nonmagnetic materials with magnetic impurities or from the loss of perfect translational order in a solid. One of the consequences of this disorder is the presence of metastable states which have extremely long relaxation times. I am currently studying the dynamics of systems with zero temperature phase transitions that involve energy barrier activation processes due to the presence of metastable states.

A study of the properties of `spin glasses' is also in progress. These are dilute alloys of magnetic impurities in non-magnetic hosts which apparently exhibit sharp phase transitions in some of their properties but not in others. There are many systems which undergo transitions called `glassy' or vitreous transitions and some of these have important applications. Usual glasses or polymer glasses are examples which are part of our everyday life. Spin glasses are believed to lie somewhere between the crystalline systems which exhibit sharp transitions and the amorphous materials which exhibit glassy transitions. A study of these systems is important for our understanding of the effects of disorder in materials.

During the past few years I have begun a study of the excitations in quantum spin systems. I have developed a method to calculate both two-magnon and three-magnon excitations in ferromagnets using real-space rescaling methods and the recursion method. The approach maps the multi-magnon problem onto an effective tight-binding Hamiltonian for general spin S and arbitrary multipole interactions between neighbouring spins. The method can be used to calculate the multi-magnon response functions directly, without the need to solve for all the eigenstates of the system. With the approach special cases which correspond to completely integrable models are easily identified. I have confirmed the earlier results of Haldane that the multi-magnon bound state branches are real and continuous across the Brillouin-zone boundary when the general spin S model is completely integrable.

I have been actively involved in the study of frustrated systems. Spin glasses are one example where frustration can either prevent a system from ordering or lead to a new type of glassy phase. My early work with A.P. Young established the result that Ising spin glasses do not order in two dimensions but do have an ordered phase in three dimensions. More recently, I have been studying purely frustrated systems without disorder. Frustration can lead to novel ground states where the symmetry of the ordered phase is no longer represented as a simple vector. The order parameter is more like a rigid body and hence the excitation spectrum is different. In addition, the symmetry of the order parameter can change the nature of the topological defects present in the system. These topological defects can interact and exhibit nontrivial unbinding transitions as the temperature increases.