The existence of a phase transition in classical antiferromagnetic models

For a wide class of antiferromagnetic models we prove the existence of a phase transition using an extended Peierls argument, taking into account a result of Dobrushin [R. L. Dobrushin, Funct. Anal. Appl. 2:44 (1968); in English, 2:302 (1968)] for an antiferromagnetic Ising model and the results of Malyshev [V. Malyshev, Comm. Math. Phys. 40:75-82 (1975)] for ferromagnetic models (such as the anisotropic rotator). In particular we review a result of Fröhlich, Israel, Lieb, and Simon [J. Fröhlich et al., J. Stat. Phys. 22(3):297-347 (198)] obtained when reflection positivity holds.