Exact solution and high temperature series expansion study of the 1/5-th depleted square lattice Ising model

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.