Volume 79, Number 2, July 2007
|Number of page(s)||5|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||21 June 2007|
Phase transition of XY model in heptagonal lattice
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
Accepted: 31 May 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.
PACS: 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
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