Partial Differential Approximants for Multicritical Singularities

A recently proposed approach—partial differential approximants—for analyzing power series in two (or more) variables for functions which exhibit singularities of multicritical, scaling character is tested by analyzing the susceptibility series for the bicritical point describing the Ising-Heisenberg-$\mathrm{XY}$ crossover in a three-dimensional classical ferromagnet. Encouraging results are obtained for the unbiased estimation of the bicritical point, of the multicritical exponents $\gamma$ and $\phi$, and of the slopes of the scaling axes.