Ising model on generalized Union Jack lattice

The Ising model is generalized to two translations on Union Jack lattice with interactions between the spins at the nearest and noncrossing diagonal neighbor sites. Exact analytical expressions are derived for the largest eigenvalue of the Kramers -Wannier transfer matrix as well as for the spontaneous magnetization, taking into account the specified interactions (six parameters of exchange interactions on the whole). The thermodynamic and frustration properties of the model are investigated. The essential features of the behavior of entropy, heat capacity and spontaneous magnetization are revealed. A number of exact expressions for phase-transition temperatures, zero-temperature entropy (residual entropy) and zero-temperature spontaneous magnetization (residual spontaneous magnetization) are obtained. Especially replete with new effects, the model under consideration manifests itself in a wide variety of special cases and relationships with other lattices, including new lattices found and not previously investigated.