The $q$ -state Potts model on the triangular lattice with both two- and three-spin interactions $K$ and $L$ (the Schick-Griffiths model) is shown to be equivalent to the $q$ -state Potts model on a 3-12 lattice with only two-spin interactions ${J}_{1}$ and ${J}_{2}$ . In particular, the ${J}_{1}>0$ and ${J}_{2}>0$ model is mapped into a Schick-Griffiths model for a range of the coupling parameters $K$ and $L$ , so that the two models are in the same universality class. We also show that a recent conjecture by Tsallis on the critical point of the 3-12 model is incorrect.The $q$-state Potts model on the triangular lattice with both two- and three-spin interactions $K$ and $L$ (the Schick-Griffiths model) is shown to be equivalent to the $q$-state Potts model on a 3-12 lattice with only two-spin interactions ${J}_{1}$ and ${J}_{2}$. In particular, the ${J}_{1}>0$ and ${J}_{2}>0$ model is mapped into a Schick-Griffiths model for a range of the coupling parameters $K$ and $L$, so that the two models are in the same universality class. We also show that a recent conjecture by Tsallis on the critical point of the 3-12 model is incorrect.

Physical review. B, Condensed matterDec 1, 19825 citations

Effect of randomness in many coupled Potts models.

Pierre Pujol

Using 2-loop renormalisation group calculations, we study a system of $N$ two-dimensional Potts models with random bonds coupled together by their local energy density. This model can be seen as a generalization of the random Ashkin-Teller model. We found that, depending on the sign of the coupling term, the universality class of the system in the presence of randomness is different. Under particular consideration, this model presents an example of a first order phase transition rounded by randomness.Using 2-loop renormalisation group calculations, we study a system of $N$ two-dimensional Potts models with random bonds coupled together by their local energy density. This model can be seen as a generalization of the random Ashkin-Teller model. We found that, depending on the sign of the coupling term, the universality class of the system in the presence of randomness is different. Under particular consideration, this model presents an example of a first order phase transition rounded by randomness.

Jan 1, 19964 citations

The

q

-state Potts model on the triangular lattice with both two- and three-spin interactions

K

and

L

(the Schick-Griffiths model) is shown to be equivalent to the

q

-state Potts model on a 3-12 lattice with only two-spin interactions

{J}_{1}

and

{J}_{2}

. In particular, the

{J}_{1}>0

and

{J}_{2}>0

model is mapped into a Schick-Griffiths model for a range of the coupling parameters

K

and

L

, so that the two models are in the same universality class. We also show that a recent conjecture by Tsallis on the critical point of the 3-12 model is incorrect.

Using 2-loop renormalisation group calculations, we study a system of

N

two-dimensional Potts models with random bonds coupled together by their local energy density. This model can be seen as a generalization of the random Ashkin-Teller model. We found that, depending on the sign of the coupling term, the universality class of the system in the presence of randomness is different. Under particular consideration, this model presents an example of a first order phase transition rounded by randomness.