The critical behavior of the 1/5-depleted square-lattice Ising model with nearest neighbor ferromagnetic interaction has been investigated by means of both an exact solution and a high-temperature series expansion study of the zero-field susceptibility. For the exact solution we employ a decoration transformation followed by a mapping to a staggered 8-vertex model. This yields a quartic equation for the critical coupling giving $K_{ c} (\equiv\beta J_{ c}) =0.695$. The series expansion for the susceptibility, to $\mathcal{ O}(K^{ 18})$, when analyzed via standard Pad\'{ e} approximant methods gives an estimate of K$_{ c}$, consistent with the exact solution result to at least four significant figures. The series expansion is also analyzed for the leading amplitude and subdominant terms.
Categories: cond-mat.stat-mech