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.

arXiv comment15 pages, 12 figures, 1 table

References in corpus (18)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Nonperturbative renormalization group approach to frustrated magnets
• Wang-Landau algorithm for continuous models and joint density of states
• Avoiding Boundary Effects in Wang-Landau Sampling
• Possible chiral phase transition in two-dimensional solid ${}^3$He
• Ising transition driven by frustration in a 2D classical model with SU(2) symmetry
• Twelve sublattice ordered phase in the J1-J2 model on the kagome lattice
• First-order transitions for n-vector models in two and more dimensions; rigorous proof
• Topology and Nematic Ordering I: A Gauge Theory
• Magnetization plateau in a two-dimensional multiple-spin exchange model
• Low temperature broken symmetry phases of spiral antiferromagnets
• Phase transition in a 2-dimensional Heisenberg model
• A Monte Carlo analysis of the phase transitions in the 2D, $J_1-J_2$ XY model
• New Universality Classes for Two-Dimensional $\sigma$-Models
• Chirality and $Z_2$ vortices in an Heisenberg spin model on the kagomé lattice
• O(N) and RP^{N-1} Models in Two Dimensions
• Monte Carlo Simulation of the Heisenberg Antiferromagnet on a Triangular Lattice: Topological Excitations
• Spin-stiffness and topological defects in two-dimensional frustrated spin systems

Cited by in corpus (7)

• The kagome antiferromagnet: a chiral topological spin liquid ?
• Gapless chiral spin liquid in a kagome Heisenberg model
• Time-reversal-symmetry-breaking chiral spin liquids: a projective symmetry group approach of bosonic mean-field theories
• Spin dynamics and disorder effects in the S=1/2 kagome Heisenberg spin liquid phase of kapellasite
• About the relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions
• Emergent Potts order in the kagomé $J_1-J_3$ Heisenberg model
• Logarithmic divergent specific heat from high-temperature series expansions: application to the two-dimensional XXZ Heisenberg model