Critical indices from perturbation analysis of the Callan-Symanzik equation

Abstract

Recent results giving both the asymptotic behavior and the explicit values of the leading-order perturbation-expansion terms in fixed dimension for the coefficients of the Callan-Symanzik equation are analyzed by the the Borel-Leroy, Padé-approximant method for the $n$-component ${\phi }^4$ model. Estimates of the critical exponents for these models are obtained for $n=0, 1, 2, \mathrm{and} 3$ in three dimensions with a typical accuracy of a few one thousandths. In two dimensions less accurate results are obtained.