Loop algorithm for classical Heisenberg models with spin-ice type degeneracy

Abstract

In many frustrated Ising models, a single-spin flip dynamics is frozen out at low temperatures compared to the dominant interaction energy scale because of the discrete "multiple valley" structure of degenerate ground-state manifold. This makes it difficult to study low-temperature physics of these frustrated systems by using Monte Carlo simulation with the standard single-spin flip algorithm. A typical example is the so-called spin ice model, frustrated ferromagnets on the pyrochlore lattice. The difficulty can be avoided by a global-flip algorithm, the loop algorithm, that enables to sample over the entire discrete manifold and to investigate low-temperature properties. We extend the loop algorithm to Heisenberg spin systems with strong easy-axis anisotropy in which the ground-state manifold is continuous but still retains the spin-ice type degeneracy. We examine different ways of loop flips and compare their efficiency. The extended loop algorithm is applied to the following two models, a Heisenberg antiferromagnet with easy-axis anisotropy along the z axis, and a Heisenberg spin ice model with the local <111> easy-axis anisotropy. For both models, we demonstrate high efficiency of our loop algorithm by revealing the low-temperature properties which were hard to access by the standard single-spin flip algorithm. For the former model, we examine the possibility of order-from-disorder and critically check its absence. For the latter model, we elucidate a gas-liquid-solid transition, namely, crossover or phase transition among paramagnet, spin-ice liquid, and ferromagnetically-ordered ice-rule state.

12 pages, 11 figures, accepted for publication in Phys. Rev. B

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• Long Range Order at Low Temperature in Dipolar Spin Ice
• Monte Carlo simulation of ice models
• Magnetization process of spin ice in a [111] magnetic field
• Finite Temperature Transitions in Large Magnetic Field in Dipolar Spin Ice
• Nematic, vector-multipole, and plateau-liquid states in the classical O(3) pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field
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Cited by in corpus (8)

• Spin-glass transition in bond-disordered Heisenberg antiferromagnets coupled with local lattice distortions on a pyrochlore lattice
• Dipolar order by disorder in the classical Heisenberg antiferromagnet on the kagome lattice
• Effect of magnetoelastic coupling on spin-glass behavior in Heisenberg pyrochlore antiferromagnets with bond disorder
• Policy Guided Monte Carlo: Reinforcement Learning Markov Chain Dynamics
• Competing Gauge Fields and Entropically-Driven Spin Liquid to Spin Liquid Transition in non-Kramers Pyrochlores
• A cluster algorithm for Monte Carlo simulations of spin ice
• A generalized Monte Carlo loop algorithm for frustrated Ising models
• Loop algorithm for classical antiferromagnetic Heisenberg models with biquadratic interactions