Disordered SU(N) antiferromagnets and the renormalization of charged instanton gases in three dimensions

Some generic properties of charged instanton gases are established in arbitrary dimension, including the fact that the self-energy, if it diverges, must diverge as the logarithm of the correlation length. A real-space renormalization is carried out in d=3 and recursion relations obtained under the assumption that the model can disorder without instantons. They reveal that for models with nontrivial Haldane phases, the correlation-length exponent is not altered by hedgehogs, and that generic instanton gases undergo first-order transitions in three dimensions. In special cases a second-order transition with continuously varying exponents is found.