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

1982; American Physical Society; Volume: 26; Issue: 3 Linguagem: Inglês

10.1103/physrevb.26.1411

1095-3795

Joan Adler, Moshe Moshe, Vladimir Privman,

Phase Equilibria and Thermodynamics

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 ${\ensuremath{\Delta}}_{1}$, the critical exponent of the confluent correction term, from relatively short series expansions is introduced and applied to $d=2$ isotropic percolation to obtain estimates of both ${\ensuremath{\Delta}}_{1}$ and $\ensuremath{\gamma}$. The discrepancies noted in the literature between values of $\ensuremath{\gamma}$ are clearly shown to be removed by the application of our method.