Numerical transfer-matrix study of surface-tension anisotropy in Ising models on square and cubic lattices
Howard L. Richards, M. A. Novotny, Per Arne Rikvold
We compute by numerical transfer-matrix methods the surface free energy \ensuremath{\tau}(T), the surface stiffness coefficient \ensuremath{\kappa}(T), and the step free energy s(T) for Ising ferromagnets with (\ensuremath{\infty}\ifmmode\times\else\texttimes\fi{}L) square-lattice and (\ensuremath{\infty}\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}M) cubic-lattice geometries, into which an interface is introduced by imposing antiperiodic or plus/minus boundary conditions in one transverse direction. These quantities occur in expansions of the angle-dependent surface tension for either rough or smooth interfaces. The finite-size scaling behavior of the interfacial correlation length provides the means of investigating \ensuremath{\tau}(T), \ensuremath{\kappa}(T), and s(T). The resulting transfer-matrix estimates are fully consistent with previous series and Monte Carlo studies, although current computational technology does not permit transfer-matrix studies of sufficiently large systems to show quantitative improvement over the previous estimates.
arXiv:cond-mat/9305010•Physical review. B, Condensed matter•Nov 15, 1993•13 citations