Question

Choose the CORRECT symmetry operations that can create all possible two dimensional planar
point groups.
(A) translation, rotation, screw, glide
(B) translation, reflection, rotation, glide
(C) screw, reflection, rotation, glide
(D) translation, reflection, screw, glide

Answer 1

Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model

Jorge V José, Leo P Kadanoff, Scott Kirkpatrick, David R Nelson

Physical Review B 16 (3), 1217, 1977

The classical planar Heisenberg model is studied at low temperatures by means of renormalization theory and a series of exact transformations. A numerical study of the Migdal recursion relation suggests that models with short-range isotropic interactions rapidly become equivalent to a simplified model system proposed by Villain. A series of exact transformations then allows us to treat the Villain model analytically at low temperatures. To lowest order in a parameter which becomes exponentially small with decreasing temperature, we reproduce …