New method for analyzing confluent singularities and its application to two-dimensional percolation

Several persistent discrepancies between different results for critical exponents of statistical-mechanical models have recently been shown to originate from inappropriate treatment of confluent singularities. In this paper a new method for evaluating ${\Delta }_1$, the critical exponent of the confluent correction term, from relatively short series expansions is introduced and applied to $d=2\mathrm{}$ isotropic percolation to obtain estimates of both ${\Delta }_1$ and $\gamma$. The discrepancies noted in the literature between values of $\gamma$ are clearly shown to be removed by the application of our method.