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We show that a continuous set of degenerate critical soft modes stronglyenhances the first-order character of a fluctuation-induced first-ordertransition in the pyrochlore dipolar Heisenberg antiferromagnet. Such adegeneracy seems essential to explain the strong first-order transitionrecently observed in Gd(2)Sn(2)O(7). We present some evidence from Monte-Carlosimulations and a perturbative renormalization group expansion.Comment: 8 pages, 9 figures, new version to appear in PRB, added ref

Degeneracy and strong fluctuation-induced first-order phase transition in the dipolar pyrochlore antiferromagnet