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We prove that various SO(n)-invariant n-vector models with interactions whichhave a deep and narrow enough minimum have a first-order transition in thetemperature. The result holds in dimension two or more, and is independent onthe nature of the low-temperature phase.

physical review letters

First-Order Transitions for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-Vector Models in Two and More Dimensions: Rigorous Proof

First-Order Transitions forn-Vector Models in Two and More Dimensions: Rigorous Proof