1208.1060 (Iwan Jensen)

Comment on `Series expansions from the corner transfer matrix
renormalization group method: the hard-squares model'    [PDF]

Iwan Jensen

Earlier this year Chan extended the low-density series for the hard-squares partition function $\kappa(z)$ to 92 terms. Here we analyse this extended series focusing on the behaviour at the dominant singularity $z_d$ which lies on on the negative fugacity axis. We find that the series has a confluent singularity of order 2 at $z_d$ with exponents $\theta=0.83333(2)$ and $\theta'= 1.6676(3)$. We thus confirm that the exponent $\theta$ has the exact value $\frac56$ as observed by Dhar.

View original: http://arxiv.org/abs/1208.1060