Exact results of a mixed spin- and spin-1 transverse Ising model with two- and four-spin interactions and crystal field on the honeycomb lattice

A mixed spin- and spin-1 transverse Ising model with two- and four-spin interactions and crystal field on the honeycomb lattice is studied using a generalized mapping transformation technique. Exact expressions for the critical temperature, the magnetization, the correlation functions, the internal energy and other thermodynamic quantities are obtained. The phase diagram is obtained as a function of the interaction parameter, crystal field or the transverse field. It is found out that the system belongs to the Onsager universality class in some region of the four-spin interaction parameter space and to the Villain–Stephenson universality class in the other region. The detailed analysis reveals that the system with nonzero transverse field is ordered regardless of the value of the crystal field.