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.
We study the critical relaxation of the two-dimensional Ising model from a fully ordered configuration by series expansion in time
t and by Monte Carlo simulation. Both the magnetization
(m) and energy series are obtained up to 12th order. An accurate estimate from series analysis for the dynamical critical exponent
z is difficult but compatible with 2.2. We also use Monte Carlo simulation to determine an effective exponent, ${z}_{\mathrm{eff}}(t)=\ensuremath{-}\frac{1}{8}d\mathrm{ln}t/d\mathrm{ln}m$, directly from a ratio of three-spin correlation to
m. Extrapolation to $\stackrel{\ensuremath{\rightarrow}}{t}\ensuremath{\infty}$ leads to an estimate $z=2.169\ifmmode\pm\else\textpm\fi{}0.003$.