Degeneracy and Strong Fluctuation-Induced First-Order Phase Transition in the Dipolar Pyrochlore Antiferromagnet

We show that a continuous set of degenerate critical soft modes strongly enhances the first-order character of a fluctuation-induced first-order transition in the pyrochlore dipolar Heisenberg antiferromagnet. Such a degeneracy seems essential to explain the strong first-order transition recently observed in Gd(2)Sn(2)O(7). We present some evidence from Monte-Carlo simulations and a perturbative renormalization group expansion.