Continuous transition between an ordered Ising magnet and a topological phase

We propose a theory of phase transitions between symmetry breaking and (intrinsic) topological phases in two-dimensional Ising spin systems. This is done by means of a parton decomposition of the Ising spins into 2N Majorana fermions, which are assumed at the mean-field level to form a Class D topological superconductor with Chern number C. Various phases are obtained by tuning C. For example, transitions between C=0,1,2 phases are described by a parton theory of massive Majorana fields coupled to an internal SO(2N) gauge field with a Chern-Simons term. Utilising various level-rank dualities of Chern-Simons-matter theories, and instanton resummation methods originally developed by 't Hooft in the solution of the U(1) problem in QCD, we demonstrate phase transitions between paramagnetic, magnetically ordered, and quantum spin liquid phases for the physical Ising spins.