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Paris S´er. I Math. : Surface group representations, Higgs bundles, and holomorphic triples. : Reduction of the Hermitian–Einstein equation on K¨ahler fiber bundles. Tohoku Math. J. : The Hitchin–Kobayashi correspondence for twisted triples. Internat. J. Math. : Flat G-bundles with canonical metrics. J. Diff. Geom. : Anti self-dual Yang–Mills connections over complex algebraic surfaces and stable vector bundles. Proc. Lond. Math. Soc. : Infinite determinants, stable bundles and curvature. Duke Math.

Math. : Stable and unitary vector bundles on a compact Riemann surface. Ann. Math. : Constructing variations of Hodge structure using Yang–Mills theory and applications to uniformization. J. Amer. Math. Soc. : Stable pairs, linear systems and the Verlinde formula. Invent. Math. : On the existence of Hermitian–Yang–Mills connections on stable bundles over compact K¨ahler manifolds. Comm. Pure and Appl. Math. H. Dijkgraaf Commun. Math. Phys. 1007/s00220-003-0867-8 Communications in Mathematical Physics Enhanced Gauge Symmetry and Braid Group Actions Balázs Szendr˝oi1,2 1 2 Department of Mathematics, Utrecht University, PO.

We prove that whenever the associated mean-field theory predicts a discontinuous transition, the actual model also undergoes a discontinuous transition (which occurs near the mean-field transition temperature), provided the dimension is sufficiently large or the first-order transition in the meanfield model is sufficiently strong. As an application of our general theory, we show that for d sufficiently large, the 3-state Potts ferromagnet on Zd undergoes a first-order phase transition as the temperature varies.