On Ground States and Phase Transitions of $\lambda$-Model on the Cayley   Tree
  In the paper, we consider the $\lambda$-model with spin values $\{1, 2, 3\}$ on the Cayley tree of order two. We first describe ground states of the model. Moreover, we also proved the existence of translation-invariant Gibb measures for the $\lambda$-model which yield the existence of the phase transition. Lastly, we established the exitance of 2-periodic Gibbs measures for the model. 
Farrukh Mukhamedov, Chin Hee Pah, Hakim Jamil
math-ph cond-mat.stat-mech math.MP