An Incompletely-Ordered Phase in the Two-Dimensional 6-State General Clock Model with Next-Nearest-Neighbor Interactions

Abstract

By applying our Monte Carlo twist method we study the Q=6 general clock model with next-nearest-neighbor interactions V_nn in two dimensions (d=2). By estmating the stiffness exponent ψ we find in some range of V_nn an ordered phase of very soft rigidity with ψ close to 0.1 less than d−1 (highest rigidity). This is a counterpart in d=2 of the incompletely-ordered phases (IOPs) with ψ\simeq1.2 already found in the same model in d=3 with V_nn=0 which has two kinds of IOPs (IOP1 and IOP2). Further analyses including the profiles of twisted states indicate that this phase is the IOP2 where a set of three adjacent states are dominant and well mixed. The phase diagram obtained looks very similar to that of the d=3 model except that the IOP1 cannot be found within the range of our study.