The critical exponent η of the planar model from one-dimensional quantum field theory

Abstract

The one-dimensional quantum field approach of Luther and Scalapino to describe the critical properties of the planar model is reviewed. The model they use is a one-dimensional spin-1 model with impurities. It is shown that the continuum limit version of this model, which is obtained by replacing the lattice by a cut-off in momentum space, does not describe the original spin-1 model, but instead a region of the phase diagram where the impurity excitations are massless. Still the results are consistent with those of Kosterlitz and Thouless if backward scattering and umklapp processes are taken into account in the derivation of the continuum limit. The critical exponent of η is equal to 1 4 at the infinite-order phase transition.