Hybrid Monte-Carlo Spin-Dynamics Simulation of Short-Range ±J Heisenberg Models with and without Anisotropy

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An efficient method of simulating Heisenberg models is developed combining the Monte-Carlo method and spin-dynamics inherent to the models. The method is applied to three-dimensional short-range ±J models with the concentration of ferromagnetic bonds p, and with and without random anisotropy to reveal effects of the anisotropy. To study their equilibrium properties, the spin-glass susceptibility x_<sg> and the absolute magnetization <∣M∣> are calculated together with the spin-glass order parameter Q(K) for a finite Monte-Carlo step K. When the anisotropy is absent, Q(K) vanishes as K increases even at very low temperatures, suggesting the absence of the spin-glass phase. This is confirmed by studying lattice size dependence of χ_<sg>. The phase diagram is also given in which the critical concentration is estimated as p_c〜0.79. When the anisotropy is present, the things change drastically. Q(K) at low temperatures reduces very little as K increases and χ_<sg>'s for different sizes of the lattice are scaled well using a scaling function with a finite transition temperature. It is concluded, hence, that a spin-glass phase transition occurs at a finite temperature. In addition, for p>p_c, a reentrant mixed phase of the ferromagnetism and the transverse spin-glass is found. Transverse random fields induced by the ferromagnetic long-range order smear the reentrant phase transition. The phase diagram thus obtained qualitatively explains experimental ones. We conclude, hence, that the anisotropy plays an essential role for the occurrence of not only the spin-glass phase but also the reentrant mixed phase.
理論物理学刊行会の論文
1993-09-25

Hybrid Monte-Carlo Spin-Dynamics Simulation of Short-Range ±J Heisenberg Models with and without Anisotropy

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