  We investigate the critical behaviour of the spectral weight of a single
quasiparticle, one of the key observables in experiment, for the particular
case of the transverse Ising model.Series expansions are calculated for the
linear chain and the square and simple cubic lattices. For the chain model, a
conjectured exact result is discovered. For the square and simple cubic
lattices, series analyses are used to estimate the critical exponents. The
results agree with the general predictions of Sachdev.
