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

Abstract

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 Padé 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.

5 pages, 2 figures

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Cited by in corpus (1)

• XXZ-Ising model on the triangular kagome lattice with spin-1 on the decorated trimers