PHASE DIAGRAMS OF POTTS MODEL WITH COMPETING BINARY-TERNARY- QUATERNARY INTERACTIONS ON CAYLEY TREE OF ORDER THREE

Abstract

We investigate the phase diagram of the Potts model with competing binary interactions J1, ternary interactions Jt, and quaternary interactions Jq on the Cayley tree of order 3. At vanishing temperature T, the phase diagram is fully determined for all values and signs of Jt/ J1, Jq/ J1 and T/ J1. The phase diagram shows the appearance of additional phases: Antiferromagnetic, Period 5, Period 7, Period 9, Period 11 and Period 12 which are in addition to the expected Ferromagnetic, Paramagnetic, Antiphase and Period 6 phases for the case of nonzero Jq for several ranges of the competing parameters. As a result, there was a significant effect of additional new phases in the phase diagrams when the order of the Cayley tree is extended up to the order 3.