Phase transition of XY model in heptagonal lattice

We numerically investigate the nature of the phase transition of the XY model in the heptagonal lattice with negative curvature, in comparison to other interaction structures such as a. at two-dimensional (2D)square lattice and a small-world network. Although the heptagonal lattice has a very short characteristic path length like the small-world network structure, it is revealed via calculation of Binder's cumulant that the former exhibits a zero-temperature phase transition while the latter has a finite-temperature transition of mean-field nature. Through the computation of the vortex density as well as the correlation function in the low-temperature approximation, we show that the absence of the phase transition originates from the strong spinwave-type fluctuation, which is discussed in relation to the usual 2D XY model. Copyright (c) EPLA, 2007.