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. Author manuscript; available in PMC: 2011 Oct 13.
Published in final edited form as: New J Phys. 2010 Sep 27;12:093044. doi: 10.1088/1367-2630/12/9/093044

Figure 3.

Figure 3

Free energy as a function of the total dipole moment per site. The curves are shifted so that the free energy of the ordered states vanishes. Dashed lines are simulation results for the full Hamiltonian. For negative values of the total dipole moment, we plot the free energy for uncorrelated defects, which have a higher free energy at vanishing dipole moment than the results for the full Hamiltonian. For positive values of the total dipole moment we show results obtained including uncorrelated defect pairs, which agree well with the simulation results.