Title : First-Order Transitions in the Presence of Continuous Symmetries

Abstract We present a number of results where there is a first-order 
transition in temperature in the presence of a continuous symmetry. 
These include strongly nonlinear nearest-neighbor 2- and 
more-dimensional vector (classical or quantum XY or Heisenberg) models, 
possibly with annealed dilution,  nematic liquid-crystal models, and 3- 
and more-dimensional lattice gauge models. A peculiar aspect of our 
results is that the proofs do not necessarily provide information on the 
nature of the low-temperature phases.