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This study present a Monte Carlo investigations of low-temperature magneticordering and phase transitions in three-state Potts model on triangular latticewith various exchange interactions between nearest (J1) and next-nearest (J2)neighbors. The density of states for varying J1 and J2 are calculated. Themagnetic structure of the ground state for various J1 and J2 are obtained. Thecritical temperature are calculated and the order of the phase transitiondetermined. The density of states difference (DOSD) and histogram analysismethod are used to investigate the order of the phase transitions. Thefrustrated regions are determined. It is shown, that for negative J1 the highdegeneration of the ground state are in fully frustrated area-1<=J2/abs(J1)<=-0.2. For positive J1 frustration are occurred in area-1<=J2/J1<=-0.5, but only in point J2/J1=-1 the system have a high degenerationand are fully frustrated. The phase diagram of the three-state triangular Pottsmodel are show.

Density of states and ground state magnetic ordering of the triangular lattice three-state Potts model