Generic First-order Phase Transition of Orientational Phases with Polyhedral Symmetry

In addition to the familiar Heisenberg magnetism, breaking of the rotational symmetry O(3) can actually lead to a large array of orientational orders, classified by three-dimensional point groups. Among this great diversity, the polyhedral orders possess most complex internal symmetries, and represent highly non-trivial ways of spontaneous symmetry breaking. In this presentation, we will utilize a recently introduced lattice Hamiltonian to study the order-disorder phase transition of those polyhedral orders. By means of Monte Carlo simulations, we find that the phase transition is generically first-order for all polyhedral symmetries. Moreover, we show that this universal result is fully consistent with our expectation from a renormalization group approach. We argue that extreme fine tuning is required to promote those transitions to second order ones. We also comment on the nature of phase transitions breaking the O(3) symmetry in general cases.