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The Heisenberg antiferromagnet on a two-dimensional triangular lattice is aparadigmatic problem in frustrated magnetism. Even in the classical limit, itsproperties are far from simple. The "120 degree" ground state favoured by thefrustrated antiferromagnetic interactions contains a hidden chiral symmetry,and supports two distinct types of excitation. And famously, three distinctphases, including a collinear one-third magnetisation plateau, are stabilisedby thermal fluctuations in applied magnetic field. The questions ofsymmetry-breaking raised by this model are deep and subtle, and after more thanthirty years of study, many of the details of its phase diagram remainsurprisingly obscure. In this paper we use modern Monte Carlo simulationtechniques to determine the finite-temperature phase diagram of the classicalHeisenberg antiferromagnet on a triangular lattice in applied magnetic field.At low to intermediate values of magnetic field, we find evidence for acontinuous phase transition from the paramagnet into the collinear one-thirdmagnetisation plateau, belonging to the three-state Potts universality class.We also find evidence for conventional Berezinskii-Kosterlitz-Thoulesstransitions from the one-third magnetisation plateau into the canted "Y-state",and into the 2:1 canted phase found at high fields. However, the phasetransition from the paramagnet into the 2:1 canted phase, while continuous,does not appear to fall into any conventional universality class. We argue thatthis, like the chiral phase transition discussed in zero field, deservesfurther study as an interesting example of a finite-temperature phasetransition with compound order-parameter symmetry. We comment on the relevanceof these results for experiments on magnetic materials with a triangularlattice.

Phase diagram of the classical Heisenberg antiferromagnet on a triangular lattice in applied magnetic field