(Fairly) Current Research Interests:
3D Plaquette Ising Model, Fractons etc
The 3D Plaquette Ising Model is a recurring theme. It first crossed the horizon in 1997 when Mariano Baig, Dominic Espriu, R.K.P.C. Malmini (a former PhD student) and myself discovered that it had a first order phase transition. This was bad news at the time, since we were looking for continuum limits which require a continuous phase transition. This was motivated by the genesis of the model in the work of Savvidy and Wegner on Gonihedric string and surface models.
Nonetheless, the dynamical properties of the model, which appeared to be glassy even in the absence of any quenched disorder, were interesting and were pursued with Adam Lipowski when he visited Heriot-Watt for a year in 1998-9.
More recent (>2014) work with Marco Mueller and Wolfhard Janke of Leipzig University found non-standard scaling behaviour at the first order transition since the the low temperature phase is highly degenerate as the result of a subsystem symmetry in the model, intermediate between a global and a local (gauge) symmetry.
Such subsystem symmetries have recently (>2016) been implicated in fractonic models, in which quasiparticle excitations display restricted (or even zero) mobility. Indeed, gauging the subsystem symmetry in the quantum 3D Plaquette Ising Model gives rise to a canonical fractonic model, the X-cube model, in much the same way as gauging the global symmetry of the standard quantum 2D Ising model gives rise to the toric code.
D. A. Johnston, M. Mueller and W. Janke, Plaquette Ising models, degeneracy and scaling, Eur. Phys. J. Special Topics, 226, Issue 4, 749–764 (2017), [arXiv:1612.00060]