One-particle dispersion and spectral weights in the transverse Ising model

The one-particle contribution to the dynamical structure factor is explored for the simple case of the transverse Ising model, using series expansion methods. The critical behavior of the spectral weight is found to conform with the general predictions of Sachdev. For the linear chain, exact results are obtained, and confirmed by correspondence with exactly known results for the correlation functions of the quantum XY model in one dimension. In higher dimensions, series are calculated for the triangular, square, and simple cubic lattices, and numerical estimates for the critical exponents are found to agree with expectations, within errors.