Earlier this year Chan extended the low-density series for the hard-squares partition function κ(z) to 92 terms. Here we analyse this extended series focusing on the behaviour at the dominant singularity zd which lies on the negative fugacity axis. We find that the series has a confluent singularity of order at least 2 at zd with exponents θ = 0.833 33(2) and θ′ = 1.6676(3). We thus confirm that the exponent θ has the exact value as observed by Dhar.
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - 21 Dec 2012|