Critical properties of the $q$ -state Potts and Potts-lattice-gas models are calculated by means of the Kadanoff variational renormalization group for dimensions 1.58, 2, and 2.32, and the Migdal approximation for arbitrary dimensions. Accurate results for the critical and tricritical exponents are obtained as well as for ${q}_{c}$ , the largest value of $q$ for which the Potts transition is continuous. It is concluded unambiguously that the three-state Potts model in three dimensions undergoes a first-order phase transition.Critical properties of the $q$-state Potts and Potts-lattice-gas models are calculated by means of the Kadanoff variational renormalization group for dimensions 1.58, 2, and 2.32, and the Migdal approximation for arbitrary dimensions. Accurate results for the critical and tricritical exponents are obtained as well as for ${q}_{c}$, the largest value of $q$ for which the Potts transition is continuous. It is concluded unambiguously that the three-state Potts model in three dimensions undergoes a first-order phase transition.

Physical review. B, Condensed matterJun 1, 198177 citations

Geometrical factor and thermal properties of a sublattice dilute Potts model

Chin‐Kun Hu

Based on the connection between a sublattice dilute q-state Potts model (SDQPM) and a correlated percolation model, we define a nonpercolating geometrical factor ${g}_{f}$ and a percolating geometrical factor ${g}_{p}$ , which depend only on q and geometrical properties of the system. The thermal properties of the SDQPM may be derived simply from ${g}_{f}$ and ${g}_{p}$ . The theory is confirmed by an exact calculation for one-dimensional SDQPM and may be extended to other interacting systems.Based on the connection between a sublattice dilute q-state Potts model (SDQPM) and a correlated percolation model, we define a nonpercolating geometrical factor ${g}_{f}$ and a percolating geometrical factor ${g}_{p}$, which depend only on q and geometrical properties of the system. The thermal properties of the SDQPM may be derived simply from ${g}_{f}$ and ${g}_{p}$. The theory is confirmed by an exact calculation for one-dimensional SDQPM and may be extended to other interacting systems.

Physical review. B, Condensed matterDec 1, 198514 citations

Specific Heat and Partition Function Zeros of the Three-state Potts Model

Seung‐Yeon Kim

Journal of the Korean Physical SocietyNov 15, 20111 citation

Algebraic properties of the 3-state Potts model

A. K. Kwaśniewski

Reports on Mathematical PhysicsOct 1, 19882 citations

Critical properties of the

q

-state Potts and Potts-lattice-gas models are calculated by means of the Kadanoff variational renormalization group for dimensions 1.58, 2, and 2.32, and the Migdal approximation for arbitrary dimensions. Accurate results for the critical and tricritical exponents are obtained as well as for

{q}_{c}

, the largest value of

q

for which the Potts transition is continuous. It is concluded unambiguously that the three-state Potts model in three dimensions undergoes a first-order phase transition.

Based on the connection between a sublattice dilute q-state Potts model (SDQPM) and a correlated percolation model, we define a nonpercolating geometrical factor

{g}_{f}

and a percolating geometrical factor

{g}_{p}

, which depend only on q and geometrical properties of the system. The thermal properties of the SDQPM may be derived simply from

{g}_{f}

and

{g}_{p}

. The theory is confirmed by an exact calculation for one-dimensional SDQPM and may be extended to other interacting systems.