Low-Temperature Series for the Correlation Length in $d=3$ Ising Model

Abstract

We extend low-temperature series for the second moment of the correlation function in $d=3$ simple-cubic Ising model from $u^{15}$ to $u^{26}$ using finite-lattice method, and combining with the series for the susceptibility we obtain the low-temperature series for the second-moment correlation length to $u^{23}$. An analysis of the obtained series by inhomogeneous differential approximants gives critical exponents $ 2\nu^{\prime} + \gamma^{\prime} \approx 2.55 $ and $ 2\nu^{\prime} \approx 1.27 $.