A Monte Carlo Simulation Study of Orientational Domain Clusters in the Planar Quadrupole Model

Abstract We have carried out a series of Monte Carlo simulations of the planar quadrupole model, using the Distributed Array Processor. A very large system size, 16 384 molecules, was employed, and special attention was given to orientational domain clustering near the order—disorder transition. Very slow fluctuations of the orientational order parameter, possibly associated with switching from one orientational domain to another, are observed. Close to the phase transition, domain clusters become extremely ramified, with highly irregular borders. On heating through the transition, the low-temperature dominant domain disappears, essentially by becoming a fractal object. The associated Hausdorff dimension decreases from D = 2 to D = 1.6 as this occurs. Although our results are consistent with a continuous, rather than a first-order, phase transition, effects of finite system size and long time scales prevent us from drawing a definite conclusion on this point.

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