Corrections to leading singularities in systems at the upper critical dimension

Abstract

Renormalisation group methods are used to calculate the behaviour of the order parameters on the coexistence curve and the critical isotherm of a one-component spin system at four dimensions, and the order parameter of a three-dimensional uniaxial dipolar ferromagnet. For the four-dimensional system, the amplitudes of the subleading corrections are obtained and found to be in disagreement with the results of a recent Monte Carlo study. The author shows how the discrepancy may be removed by fitting the Monte Carlo data to a crossover scaling function for the order parameter rather than to an asymptotic form. For the three-dimensional system the amplitude of the subleading correction is found to be in reasonable agreement with experimental results on the uniaxial dipolar ferromagnet LiHoF4.