A check of a D = 4 field-theoretical calculation using the high-temperature expansion for Dysonʹs hierarchical model Original Research Article

We calculate the high-temperature expansion of the two-point function up to order 800 in β. We show that estimations of the critical exponent γ based on asymptotic analysis are not very accurate in the presence of confluent logarithmic singularities. Using a direct comparison between the actual series and the series obtained from a parametrization of the form (βc−β)−γ(ln(βct-β)p+r), we show that the errors are minimized for γ = 0.9997 and p = 0.3351, in very good agreement with field-theoretical calculations. We briefly discuss the related questions of triviality and hyperscaling.