General quadratic Hamiltonian models, describing interaction between crystalmolecules (typically with $D_{2h}$ symmetry) take into account couplingsbetween their uniaxial and biaxial tensors. While the attractive contributionsarising from interactions between similar tensors of the participatingmolecules provide for eventual condensation of the respective orders atsuitably low temperatures, the role of cross-coupling between unlike tensors isnot fully appreciated. Our recent study with an advanced Monte Carlo technique(entropic sampling) showed clearly the increasing relevance of this cross termin determining the phase diagram, contravening in some regions of modelparameter space, the predictions of mean field theory and standard Monte Carlosimulation results. In this context, we investigated the phase diagrams and thenature of the phases therein, on two trajectories in the parameter space: oneis a line in the interior region of biaxial stability believed to berepresentative of the real systems, and the second is the extensivelyinvestigated parabolic path resulting from the London dispersion approximation.In both the cases, we find the destabilizing effect of increased cross-couplinginteractions, which invariably result in the formation of local biaxialorganizations inhomogeneously distributed. This manifests as a small, butunmistakable, contribution of biaxial order in the uniaxial phase.The freeenergy profiles computed in the present study as a function of the two dominantorder parameters indicate complex landscapes, reflecting the difficulties inthe ready realization of the biaxial phase in the laboratory.
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