Phase transition of XY model in heptagonal latticeS. K. Baek1, P. Minnhagen2 and B. J. Kim1
1 Department of Physics, BK21 Physics Research Division, and Institute of Basic Science, Sungkyunkwan University - Suwon 440-746, Republic of Korea
2 Department of Theoretical Physics, Umeå University - 901 87 Umeå, Sweden
received 6 April 2007; accepted in final form 31 May 2007; published July 2007
published online 21 June 2007
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 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 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.
64.60.Cn - Order-disorder transformations; statistical mechanics of model systems.
89.75.Hc - Networks and genealogical trees.
74.50.+r - Tunneling phenomena; point contacts, weak links, Josephson effects.
© Europhysics Letters Association 2007