2008/09/12 by J. S. Valverde, J.S. Valverde, Onofre Rojas +1 · 2 citations
Mathematics · Physics and Astronomy · #Opinion Dynamics and Social Influence #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.79.041101
5 pages, 5 figures
arxiv created 2008/09/12 · openalex publication_date 2009/04/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study a two-dimensional XXZ -Ising model on a square-hexagon (denoted for simplicity by 4-6) lattice with spin 1/2. The phase diagram at zero temperature is discussed, where five states are found, two types of ferrimagnetic states, two types of antiferromagnetic states, and one ferromagnetic state. To solve this model, we have mapped onto the eight-vertex model with union Jack interaction term, and it was verified that the model cannot be completely mapped onto eight-vertex model. However, by imposing an exact solution condition, we have found the region where the XXZ -Ising model on 4-6 lattice is exactly soluble with one free parameter, particularly for the case of symmetric eight-vertex model condition. In this manner we have explored the properties of the system and have analyzed the interacting competition parameters which preserve the region where there is an exact solution. Unfortunately the present model does not satisfy the free fermion condition of the eight-vertex model, unless for a trivial solution. Even so, we are able to discuss the critical point region, beyond the region of exact resolvability.