Phase transitions in fully frustrated spin systems

Abstract

We study the phase structure and critical behavior of fully frustrated systems. The Hamiltonians considered have global O(n) symmetry, as well as the discrete symmetries associated with the space group. The fully frustrated XY (n=2) model on the square and triangular lattices are two of the more popular models that belong to this class of problems. We derive a Landau-Ginzburg Hamiltonian for the general case, assuming that both the (continuous) O(n) symmetry, and some discrete symmetry are broken in the low-temperature phase. This Hamiltonian is studied in 4-ε and 2+ε dimensions by standard renormalization-group procedures. For n=d=2 we establish connection to a microscopic double-layer model, which is mapped onto a Coulomb-gas problem. Renormalization-group recursion relations are derived, and the resulting flows are used to restrict the kinds of transitions that can be observed in various cases. In particular, for the fully frustrated XY model on the square and triangular lattices, we expect a single transition from the disordered phase to one with Ising-like long-range order and algebraically decaying XY-type correlations.