Structure and Dynamics Group

Abstract

We use the the scale invariant scattering formalism to determine the renormalization group fixed points of two-dimensional critical systems. Scale invariance in two dimensions generalizes to conformal symmetry which imposes sufficient conditions that allows us to solve for the scattering amplitudes of the underlying excitations at criticality. The resulting equations allows for generalizing the symmetry parameter to continuous values which gives access to critical points of geometric phase transitions. For systems with quenched disorder, the field theory picture is retrieved by using replica trick at the expense of dealing with multiple copies of the system. We used this method to determine exactly the random fixed points of disordered O(N) and Potts models. For systems with local symmetry, we construct particles to resemble the order parameter with non-vanishing expectation value in the ordered phase. This is implemented for both RPᴺ⁻¹ and CPᴺ⁻¹ models to gain insight into possible quasi-long-range ordering (QLRO) similar to the Berezinskii-Kosterlitz-Thouless (BKT) line of fixed points present in O(2). For the coupled systems, we introduce new amplitudes corresponding to scattering of particles across the two coupled systems. This was done for a vector O(N) coupled to an Ising Z₂ model and for coupled q-state and r-state Potts models to investigate as a special case the fully frustrated XY (FFXY) model and correlated percolation respectively.