Theoretical Physics Technical Talk

My research focuses on the statistical mechanics of condensed matter systems--- particularly in settings involving the interplay of strong correlations and lattice geometry--- with a concurrent emphasis on computational methods. I will begin with a brief overview of my past and current work, and then focus on the statistical mechanics of classical hardcore dimers on the quasiperiodic Ammann–Beenker tiling for the rest of the talk.
After describing the structure of the configuration space, I will present an explicit real-space renormalization group transformation to analyse its statistical mechanics. The resulting RG analysis reveals an interacting fixed point lacking continuous translational and rotational symmetries, and exhibiting discrete rather than continuous scale invariance. The fixed-point theory is itself a hardcore dimer model, in contrast to periodic bipartite lattices, which admit effective continuum descriptions. I will show that this discrete scale invariance leads to log-periodic modulations of familiar critical power laws.