On the topological phase transition of the two-dimensional XY-model on the Voronoi-Delaunay lattice

We numerically investigate the static properties of the two-dimensional (2D) XY-model on the Voronoi-Delaunay lattice, with average connectivity (k) over bar similar to 6. The critical temperature, magnetization and vortex density are obtained. For instance, in this lattice the critical temperature, above which free vortices take place, reads T-cr(VD) approximate to 1.22 ( in units of J, the exchange constant), higher than their counterparts for regular square, T-cr(SL) approximate to 0.79, and triangular lattices T-cr(TL) approximate to 1.156, with constant connectivity given by 4 and 6, respectively. Such results lead us to argue that not only the connectivity number but also how the sites are distributed and linked among themselves is also important for determining these physical quantities.