Borel summation of the dynamic index z in the model A of critical dynamics with an account of the strong coupling asymptotics

Abstract

In this paper we consider the model A of critical dynamics which describes the dynamic characteristics of the critical behavior of ferromagnets as well as other systems with a nonconserved order parameter. For such a model the renormalization group method and the ε-expansion are the common tool for constructing consistent perturbative expansion for critical exponents and other universal quantities. One of the problems in this formalism is the asymptotic nature of the series obtained within the ε-expansion, so to get reliable theoretical predictions it is necessary to apply the Borel resummation technique. In this work we apply such a resummation technique to the four-loop ε-expansion of the dynamical exponent z which describes the critical slowing down in the ferromagnet-type systems. The motivation of the paper is twofold: 1) improved values for the coefficients of the ε-expansion have recently been obtained, 2) sit has been shown that incorporation of strong coupling asymptotics into the Borel resummation technique leads to better convergence of the resummation procedure for static models. In this investigation it was shown that taking into account the asymptotics of the strong coupling for critical static problems also improves the predictions of the higher terms of the series. Since the strong-coupling asymptotic for this model is unknown, this parameter is held free and adjusted in accordance with the condition of the most accurate prediction of the last known term from the previous ones and the rate of convergence of the procedure.