Phase transition of $XY$ model in heptagonal lattice
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
We numerically investigate the nature of the phase transition of the $XY$ model
in the heptagonal lattice with the negative curvature, in comparison
to other spatial interaction structures such as a flat 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 the Binder's cumulant
that the former exhibits a zero-temperature phase transition while the
latter has the finite-temperature transition of the 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.