LIFSHITZ POINTS IN ISING SYSTEMS

Phase diagrams of Ising systems with competing interactions are calculated using (a) the method of Müller-Hartmann and Zittartz to determine the transition temperature via the vanishing of an interface free energy (b) a Migdal-Kadanoff bond-moving scheme and (c) Monte Carlo simulations. It is shown that in two-dimensional Ising systems a uniaxial Lifshitz point can exist at non-zero temperatures, whereas the lower critical dimension dl for a Lifshitz point in a system with identical competing interactions along each of its cartesian axis is dl≧2. © 1979 Springer-Verlag.