Volume 78, Number 1, April 2007
|Number of page(s)||6|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||22 March 2007|
Interface tension of the square lattice Ising model with next-nearest-neighbour interactions
Institut für Theoretische Physik and Centre for Theoretical Sciences (NTZ), Universität Leipzig - Postfach 100 920, D-04009 Leipzig, Germany
Accepted: 19 February 2007
In a recent letter, Zandvliet (Europhys. Lett., 73 (2006) 747) presented a simple derivation of an analytical expression for the interface free energy in the (10) direction of the Ising model on a square lattice with nearest- and next-nearest-neighbour couplings, reproducing the famous exact Onsager formula in the special case of only nearest-neighbour interactions. By comparing the resulting transition temperatures, determined as the point where the interface tension vanishes, with previous numerical results in the literature, support for the validity of the new analytical formula in the general case was claimed. Guided by the fact that Zandvliet's simple, but rather heuristic derivation neglects overhang configurations and bubble excitations completely, we show that his approach is equivalent to the classic solid-on-solid (SOS) approximation which is known to reproduce accidentally the exact interface tension along one of the two main axes in the case of only nearest-neighbour interactions. In the limiting situation where only next-nearest-neighbour interactions are considered, we prove analytically that such a coincidence no longer holds. To assess the accuracy of Zandvliet's formula for the general model we have performed a careful computer simulation study using multicanonical and cluster Monte Carlo techniques combined with finite-size scaling analyses. Our results for the hitherto unknown interface tension and the transition temperatures show that the analytical formula yields fairly good approximations but, in general, is not exact.
PACS: 68.35.Rh – Phase transitions and critical phenomena / 02.70.Uu – Applications of Monte Carlo methods / 75.10.Hk – Classical spin models
© Europhysics Letters Association, 2007
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.