Continued fraction coherent anomaly approach for Blume-Capel model

Abstract

The continued fraction coherent anomaly method (CAM) is applied to study the criticality of the Blume-Capel model. For comparison, we present also the power series approach with a different way of calculating the critical coefficients. The variation of the Curie temperature Tc with respect to the single-ion anisotropy parameter D/J (where D is the single-ion anisotropy and J is the nearest-neighbour exchange constant) is studied using both methods. The method of continued fraction CAM approach consists in expressing the high-temperature static susceptibility series in the form of a continued fraction and subsequently in finding the roots of different order approximants, which are then used in analysing the critical data. The magnitude of confluent singularities has been estimated by the continued fraction CAM approach and the results are compared with those obtained from power series CAM approach.