Low-temperature recursion relations and high-temperature series expansions

We suggest that renormalization-group recursion relations can profitably be combined with high-temperature series expansions in systems with critical points at zero temperature. Low-temperature recursion relations are integrated out to high temperatures, where conventional high-temperature series should accurately describe quantities such as the susceptibility. A "variational" principle is suggested which gives the optimal temperature at which to splice together the low- and high-temperature results. In this way, we obtain a sequence of approximants to the susceptibility of the classical two-dimensional Heisenberg model which apparently converges exponentially fast at all temperatures. Although further investigation reveals that these approximants are not as accurate as their exponential convergence suggests, they do appear to give a good quantitative description at all temperatures of the susceptibilities we have studied.