Monte Carlo Simulation of the Heisenberg Antiferromagnet on a Triangular Lattice: Topological Excitations

Abstract

We have simulated the classical Heisenberg antiferromagnet on a triangular lattice using a local Monte Carlo algorithm. The behavior of the correlation length $\xi$, the susceptibility at the ordering wavevector $\chi (\mathbf{Q})$, and the spin stiffness $\rho$ clearly reflects the existence of two temperature regimes -- a high temperature regime $T>T_{th}$, in which the disordering effect of vortices is dominant, and a low temperature regime $T<T_{th}$, where correlations are controlled by small amplitude spin fluctuations. As has previously been shown, in the last regime, the behavior of the above quantities agrees well with the predictions of a renormalization group treatment of the appropriate nonlinear sigma model. For $T>T_{th}$, a satisfactory fit of the data is achieved, if the temperature dependence of $\xi$ and $\chi (\mathbf{Q})$ is assumed to be of the form predicted by the Kosterlitz--Thouless theory. Surprisingly, the crossover between the two regimes appears to happen in a very narrow temperature interval around $T_{th}\simeq 0.28$.

13 pages, 8 Postscript figures

References in corpus (3)

• The s=1/2 Heisenberg Antiferromagnet on the Triangular Lattice: Exact Results and Spin-Wave Theory for Finite Cells
• The Heisenberg antiferromagnet on a triangular lattice: topological excitations
• Monte Carlo Calculation of the Spin-Stiffness of the Two-Dimensional Heisenberg Model

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