Thermal destruction of chiral order in a two-dimensional model of coupled trihedra

Abstract

We introduce a minimal model describing the physics of classical two-dimensional (2D) frustrated Heisenberg systems, where spins order in a non-planar way at T=0. This model, consisting of coupled trihedra (or Ising-$\mathbb{R}{P}^3$ model), encompasses Ising (chiral) degrees of freedom, spin-wave excitations and ${\mathbb{Z}}_2$ vortices. Extensive Monte Carlo simulations show that the T=0 chiral order disappears at finite temperature in a continuous phase transition in the 2D Ising universality class, despite misleading intermediate-size effects observed at the transition. The analysis of configurations reveals that short-range spin fluctuations and ${\mathbb{Z}}_2$ vortices proliferate near the chiral domain walls explaining the strong renormalization of the transition temperature. Chiral domain walls can themselves carry an unlocalized ${\mathbb{Z}}_2$ topological charge, and vortices are then preferentially paired with charged walls. Further, we conjecture that the anomalous size-effects suggest the proximity of the present model to a tricritical point. A body of results is presented, that all support this claim: (i) First-order transitions obtained by Monte Carlo simulations on several related models (ii) Approximate mapping between the Ising-$\mathbb{R}{P}^3$ model and a dilute Ising model (exhibiting a tricritical point) and, finally, (iii) Mean-field results obtained for Ising-multispin Hamiltonians, derived from the high-temperature expansion for the vector spins of the Ising-$\mathbb{R}{P}^3$ model.

15 pages, 12 figures, 1 table