Journal of Statistical Physics, Vol. 109, Nos. 1/2, October 2002. p. 133-142.
Properties of the two dimensional Ising model with fixed magnetization are deduced from known exact results on the two dimensional Ising model. The existence of a continuous phase transition is shown for arbitrary values of the fixed magnetization when crossing the boundary of the coexistence region. Modifications of this result for systems of spatial dimension greater than two are discussed.