High-temperature critical behavior of two-dimensional planar models: A series investigation

We have analyzed new twelfth-order high-temperature series for the susceptibility and correlation length of classical planar models on the triangular lattice using an $n$-fit method of analysis tailored to the form of the singularity $A\exp \left(b{t}^{-\nu }\right)$ predicted by Kosterlitz and Thouless. Test-function analysis shows that the $n$-fit method is significantly more reliable in treating a number of possible corrections to the leading singularity than is the $D$ log Padé analysis of the logarithm and logarithmic derivative used in earlier series work on tenth-order series. Our $n$-fit analysis leads to the results $\nu =0.5\mathrm{}\pm 0.1$ and $\eta =0.27\mathrm{}\pm 0.03$ in good agreement with the Kosterlitz-Thouless predictions $\nu =\frac{1}{2}$ and $\eta =\frac{1}{4}$.