Berezinskii-Kosterlitz-Thouless phase transition in systems with exotic symmetries

A Berezinksii-Kosterlitz-Thouless phase transition in systems with the exceptional symmetry groups G=E _6,7,8, G ₂, and F ₂ is studied. The critical exponents and the exponents of the logarithmic corrections to the correlation functions at the transition point are found by the renormalization-group method. It is shown that for G=A, D, and E the critical exponents can be expressed in terms of the Coxeter numbers h _G (or the values of the Casimir operator in the adjoint representation K ₂ ^G ). Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 743–747 (10 May 1996)