Critical properties of two-dimensional models

Critical properties of two-dimensional classical models and (1 + 1)-dimensional quantum models are obtained by solving a general dimerized spin chain. The staggered-electric exponent of the $F$ model is derived. The central role of umklapp scattering in controlling renormalization and determining Potts-model critical exponents is pointed out. The thermal exponent of the Potts model is evaluated, and the validity of den Nijs conjecture is established. Logarithmic singularities at the multicritical point are obtained.