Exact solution and high-temperature series expansion study of the one-fifth-depleted square-lattice Ising model

The critical behavior of the one-fifth-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 eight-vertex model. This yields a quartic equation for the critical coupling giving Kc(≡βJc)=0.695. The series expansion for the susceptibility, to O(K18), when analyzed via standard Padé approximant methods gives an estimate of Kc, 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.