A Check of a D=4 Field-Theoretical Calculation Using the High-Temperature Expansion for Dyson's Hierarchical Model

Abstract

We calculate the high-temperature expansion of the 2-point function up to order 800 in beta. We show that estimations of the critical exponent gamma based on asymptotic analysis are not very accurate in presence of confluent logarithmic singularities. Using a direct comparison between the actual series and the series obtained from a parametrization of the form (beta_c -beta)^(-gamma) (Ln(beta_c -beta))^p +r), we show that the errors are minimized for gamma =0.9997 and p=0.3351, in very good agreement with field-theoretical calculations. We briefly discuss the related questions of triviality and hyperscaling