Open AccessPotts Model with Competing Binary-Ternary-Quaternary Interactions on Cayley Tree
Author(s) -
Nasir Ganikhodjaev,
Mohd Hirzie Mohd Rodzhan,
Nurul Farahana Ififi Omar Baki
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1489/1/012023
Subject(s) - ternary operation , phase diagram , potts model , quaternary , binary number , antiferromagnetism , phase (matter) , tree (set theory) , mathematics , binary tree , statistical physics , thermodynamics , phase transition , condensed matter physics , physics , combinatorics , computer science , quantum mechanics , geology , paleontology , arithmetic , programming language
We study the phase diagrams for the Potts model with competing binary, ternary and quaternary interactions on Cayley tree of order 2. At vanishing temperature T, the phase diagram is fully determined for all values of competing binary, ternary and quaternary interactions. We extend the results (for the case J q = 0) obtained by Ganikhodjaev et. al. [9]. The results show that the appearance of addition phases: antiferromagnetic and Period 6, in the case of nonzero quaternary interactions for several ranges. Then, we investigate the modulated phase, with the phase being indicated by many different types of commensurate and incommensurate phases by plotting the wavevectors versus temperature. Lastly, the Lyapunov exponent is used to verify the stability of the periods.