A numerical study of the zeroes of the grand partition function of hard needles of length $k$ on stripes of width $k$

Abstract

We numerically study zeroes of the partition function for trimers ($k = 3$) on $3 \times L$ strip. While such results for dimers ($k = 2$) on 2D lattices are well known to always lie on the negative real axis and are unbounded, here we see that the zeroes are bounded on branches in a finite-sized region and with a considerable number of them being complex. We analyze this result further to numerically study the density of zeroes on such branches, estimating the critical power-law exponents, and make interesting observations on density of filled sites in the lattice as a function of activity $z$.