Correlation functions on the critical line of the two-dimensional planar model: Logarithms and corrections to scaling
Correlation functions are calculated on the critical line of the planar or XY model. A crossover is found between simple scaling behavior for 2 πKeff > 4 and more complex scaling behavior for 2 πKeff = 4. At the Kosterlitz-Thouless critical point, 2 πKeff = 4, logarithmic factors appear in the correlation functions. These corrections to simple scaling behavior are calculated for many correlation functions, including correlation functions not previously studied. The calculation is carried out in the closely related generalized Villain model using a combination of perturbation and renormalization techniques.