Journal of Statistical Physics, Vol. 29, No. 2, 1982. p. 231-245.
In the parameter space of systems with competing interactions there are specific trajectories called order (disorder) lines. Along these trajectories the competition between the different interactions effectively reduces the dimensionality of the system and the model can be exactly solved. It is shown that the order (disorder) trajectories end up at a multicritical point. The method of Peschel and Emery is used to determine the (anisotropic) critical behavior of the spin-spin correlation functions near the multicritical point. The quantum spin systems discussed here include the XYZ chain in a field, the straggered XYZ chain in a field, and a
Hamiltonian version of a three-dimensional Ising model with biaxial competing interactions.