Review Reports

Round 1

Reviewer 1 Report

I wish the author good luck in his future scientific work. My suggestion is that for the SOS model, it would be good to study the problem with q states.

Author Response

Dear Reviewer,

thank you for your comments. 

In Remark 1, we have mentioned about the SOS model which is a particular case of the λ-model. However, in Remark 3, it is point out that for the SOS model the disordered phase does not exist in the sense of this paper. However, it is given an example (after that Remark) for which the disordered phase exists.

 

 

 

Reviewer 2 Report

A lambda-model with 3 states is studied on the Cayley tree. As emphasized by the author, this model is more general than the 3-state Potts model. The author could also mention in the introduction the Clock model defined by \lambda(x,y)=cos(2\pi(x-y)/q). From the physics perspective, this model is equivalent to the Potts model in the case q=3. Both models undergo a phase transition between a ferromagnetic and a paramagnetic phase belonging to the same universality class. I guess that it is also the case for the model studied by the author. I would therefore recommend the author to explain why his model is worth studying.

Author Response

Dear Reviewer,

thank you for your comments. We have added a sentence in section "Introduction" about the clock model.