Approximation theory

Daghestan Electronic Mathematical Reports: Issue 17 (2022)

Phase diagram and structure of the ground state of the three-vertex Potts model on the Kagome lattice

UDK: 537.9

Pages: 53 - 66

The high-efficient Wang-Landau algorithm of the Monte-Carlo entropic method has used for studies the three-state Potts model on the Kagome lattice, taking into account the ferromagnetic exchange interaction between the nearest neighbors and the competing antiferromagnetic interaction between the next nearest neighbors. The density of states are calculated, the magnetic structures of the ground state are determined and the temperature dependences of various thermodynamic parameters are calculated. It is shown that depending on the ratio of interactions between the nearest and next nearest neighbors, the ground state of the system can be ferromagnetic, highly degenerated frustrated or have a special type of triplet antiferromagnetic ordering. It was established that the phase transition from the ferromagnetic phase to the paramagnetic is the phase transition of the second order, while the transition from the triplet antiferromagnetic phase is the first order. At the frustration point, which divides both regions, the phase transitions does not occur (the system does not go to ordered phase for any temperature close to zero). The critical temperature of the phase transitions calculated and phase diagram of the system are determined.

Keywords: Potts model, density of states, Kagome lattice, ground state structures, entropy, frustration, phase transition, phase diagram, Monte Carlo method, Wang-Landau algorithm.

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