Phase transitions in two-dimensional systems

Abstract

Relations between two-dimensional physical systems, continuous-spin Hamiltonians, and discrete spin or Potts models are established by Landau symmetry and renormalization-group arguments. Experimental realizations of XY and Heisenberg models with cubic anisotropy as well as of different Potts models are reviewed. Then a unified model encompassing these classes of models is introduced. For the special case of a six-state discrete model a phase diagram is proposed based on duality and Migdal renormalization-group transformations.