First-order transition and tricritical behavior of the transverse crystal field spin-1 Ising model

•In this paper we have studied the phase transition in quantum model.•The model presents second and first-order phase transitions.•The tricritical behavior in the phase diagram was analyzed.

The phase diagram of the spin-1 Ising model in the presence of a transverse crystal-field anisotropy (Dx) is studied within the framework of an effective-field theory with correlation. The effect of the coordination number (z  ) on the phase diagram in the T–DxT–Dx plane is investigated. We observe only second-order transitions for coordination number z<7z<7, while that for z≥7z≥7 we have first- and second-order transitions, with the presence of two tricritical points. The lower tricritical temperature (Tt) decreases monotonically with the increasing value of z  , and in the limit of z→∞z→∞ we found Tt=0Tt=0, corresponding to the mean-field solution [Ricardo de Sousa and Branco, Phys. Rev. E 77 (2008) 012104] with a single tricritical point in the phase diagram.