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Springer eBooks

Generalizations and applications of Callan-Symanzik equations to statistical mechanics in critical phenomena

Yoshitake Yamazaki

Published Oct 29, 2005• 1 citation
Publisher
DOI
10.1007/bfb0013355

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The coefficients in the Callan-Symanzik equations for a three-dimensional, continuous spin Ising model with an $\mathrm{exp}(\ensuremath{-}A{s}^{4}+B{s}^{2})$ spin-weight factor are expanded in the dimensionless, renormalized coupling constant. These series are summed by the Pad\'e-Borel method to yield the critical indices $\ensuremath{\gamma}=1.241\ifmmode\pm\else\textpm\fi{}0.002$, $\ensuremath{\eta}=0.02\ifmmode\pm\else\textpm\fi{}0.02$, $\ensuremath{\nu}=0.63\ifmmode\pm\else\textpm\fi{}0.01$, and ${\ensuremath{\Delta}}_{1}=0.49\ifmmode\pm\else\textpm\fi{}0.01$.