The classical $J_1$-$J_2$ Heisenberg model on the Kagome lattice

Abstract

Motivated by earlier simulated annealing studies and materials with large spin on the Kagome lattice, we performed large scale parallel tempering simulations on the Kagome lattice for the extended classical Heisenberg model including next nearest neighbor interactions. We find that even a small inclusion of a $J_2$ term induces anti-ferromagnetic order which prevails in the thermodynamic limit. The magnitude of this effect is surprising. While at $J_2=0$ the finite-size behaviour does not suggest a phase-transition, at other points the numerical result is consistent with one. Close to $J_2=0$ and for a positive sign of $J_2$ two subsequent phase-transitions/crossovers are found, one of them connecting to the crossover for the $J_2=0$ case, shedding light to the pure case. The universality classes of the transitions were explored.

8 pages, 10 figures

References in corpus (9)

• Parallel Tempering: Theory, Applications, and New Perspectives
• The ALPS project release 1.3: open source software for strongly correlated systems
• The ALPS project release 2.0: Open source software for strongly correlated systems
• Feedback-optimized parallel tempering Monte Carlo
• Spin waves in the Frustrated Kagome Lattice Antiferromagnet KFe3(OH)6(SO4)2
• Octupolar ordering of classical kagome antiferromagnets in two and three dimensions
• Make life simple: unleash the full power of the parallel tempering algorithm
• Magnetic phase diagrams of classical triangular and kagome antiferromagnets
• Order by disorder, without order, in a two-dimensional spin system with O(2) symmetry

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• Ising chains with competing interactions in presence of long-range couplings
• Monte Carlo study on low-temperature phase diagrams of the $J_1$-$J_2$ classical $XY$ kagome antiferromagnet
• Robust semiclassical magnetization plateau in the kagome lattice