Ising transition in frustrated Heisenberg models

Abstract

We derive scaling equations for a 2D square Heisenberg model where frustration spontaneously breaks the ${Z}_{4}$ lattice symmetry. At short distances, the model behaves as two interpenetrating N\'eel sublattices. Short-wavelength fluctuations couple these sublattices, driving a crossover to single-lattice behavior at long distances and generating an Ising order parameter. When the spin-correlation and crossover lengths become comparable, there exists a finite-temperature Ising phase transition independent of the subsequent development of a sublattice magnetization.