We investigate the emergence of a myriad of phases in the strong coupling regime of the dipolar Hubbard model in two dimensions. By using a combination of numerically unbiased methods in finite systems with analytical perturbative arguments, we show the versatility that trapped dipolar atoms possess in displaying a wide variety of many-body phases, which can be tuned simply by changing the collective orientation of the atomic dipoles. We further investigate the stability of these phases to thermal fluctuations in the strong coupling regime, highlighting that they can be accessed with current techniques employed in cold atoms experiments on optical lattices. Interestingly, both quantum and thermal phase transitions are signalled by peaks or discontinuities in local moment-local moment correlations, which have been recently measured in some of these experiments, so that they can be used as probes for the onset of different phases.
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