A Monte Carlo study of the first-order transition in a Heisenberg FCC antiferromagnet

A nearest neighbor Heisenberg antiferromagnet on a face-centered cubic lattice is studied by extensive Monte Carlo simulations in zero magnetic field. The parallel tempering algorithm is utilized, which allows one to overcome a slow relaxation of the magnetic order parameter and to fully equilibrate moderately sized clusters with up to N ? 7 × 10³ spins. By collecting energy and order parameter histograms on clusters with up to N ? 2 × 10⁴ sites, we accurately locate the first-order transition point at T _c = 0.4459(1)J.     

Comparative study between a two-dimensional anisotropic Heisenberg antiferromagnet with easy-axis single-ion anisotropy and one with easy-axis exchange anisotropy

Generally, in literature, easy-axis single ion anisotropy and easy-axis exchange anisotropy was treated in indistinct way. In this work we propose to perform a comparative study of the effects of these two easy-axis anisotropies on the behavior of the magnetization and the critical temperature (_Tc)$(T_{\mathrm{c}})$ in the 2D classical Heisenberg antiferromagnetic model. In order to study the low-temperature thermodynamics of this model, we should consider the contribution of anisotropic spin waves, using a self-consistent harmonic approximation (SCHA) theory. We compare the predictions of SCHA with numerical simulations on L×L$L\times L$ square lattices using Monte Carlo (MC) simulations, which include effects due to all thermodynamically allowed excitations. Our SCHA results are in good agreement with our MC simulations results and have shown that the strong K$K$ limit gives two different Ising-like behavior. In the exchange anisotropic case, the dependence of _Tc$T_{\mathrm{c}}$ on anisotropic parameter K$K$ becomes linear and in the single-ion anisotropic case, _Tc$T_{\mathrm{c}}$ becomes independent of K$K$. Also, using MC simulations and finite size scaling, we show that the critical exponents in the two anisotropic case are compatible with the 2D Ising values α=0.125$\alpha =0.125$ and γ=1.75$\gamma =1.75$.     

Short-range order in a hexagonal Heisenberg antiferromagnet: β-oxygen

We have considered a hexagonal Heisenberg antiferromagnet with interplane exchange parameter J₂ which is small compared to the in-plane exchange parameter J₁. It is shown that the ratio of these parameters determines the degree of short range within the hexagonal plane. In connection the magnetic structure of solid β-oxygen is discussed.     

Error Estimation in the Histogram Monte Carlo Method

We examine the sources of error in the histogram reweighting method for Monte Carlo data analysis. We demonstrate that, in addition to the standard statistical error which has been studied elsewhere, there are two other sources of error, one arising through correlations in the reweighted samples, and one arising from the finite range of energies sampled by a simulation of finite length. We demonstrate that while the former correction is usually negligible by comparison with statistical fluctuations, the latter may not be, and give criteria for judging the range of validity of histogram extrapolations based on the size of this latter correction.     

Monte Carlo simulation of a random-field Ising antiferromagnet

Phase transitions in the three-dimensional diluted Ising antiferromagnet in an applied magnetic field are analyzed numerically. It is found that random magnetic field in a system with spin concentration below a certain threshold induces a crossover from second-order phase transition to first-order transition to a new phase characterized by a spin-glass ground state and metastable energy states at finite temperatures.     

A quantum Monte Carlo study of the localizable entanglement in anisotropic ferromagnetic Heisenberg chains

We study the localizable entanglement in large one-dimensional anisotropic XYZ ferromagnetic Heisenberg chains interacting with a uniform magnetic field. With the use of quantum Monte Carlo simulations we calculate the bounds of localizable entanglement by means of the correlation functions. The present quantum Monte Carlo method has the advantage over existing methods that it can be readily applied to fully anisotropic magnetic chains.     

A Theory on Flat Histogram Monte Carlo Algorithms

The flat histogram Monte Carlo algorithms have been successfully used in many problems in scientific computing.However, there is no a rigorous theory for the convergence of the algorithms. In this paper, a modified flat histogram algorithm is presented and its convergence is studied. The convergence of the multicanonical algorithm and the Wang-Landau algorithm is argued based on their relations to the modified algorithm. The numerical results show the superiority of the modified algorithm to the multicanonical and Wang-Landau algorithms. PACS number: 02.70.Tt, 02.50.Ng     

A Monte Carlo study of two-dimensional classical easy-plane Heisenberg models with symmetry-breaking

Monte Carlo studies of thermodynamic functions for quasi-2-dimensional classical ferromagnets are reported. Easy-plane Heisenberg models with Ising and 6-fold symmetry breaking fields in the easy-plane are emphasized as models of Rb₂CrCl₄ and CoCl₂-intercalated graphite.     

六方晶格基底上薄膜生长的Monte Carlo模拟研究

利用Monte Carlo（MC）方法,模拟研究了六方晶格基底上薄膜生长的初始阶段岛的形貌和岛的尺寸与薄膜覆盖度以及入射粒子沉积速率之间的关系. 结果表明在基底温度为300K时,岛的形貌主要表现为分形生长,随着薄膜覆盖度的增加,岛的分形枝簇变大,岛的数目不断减少. 在同样的温度下,随着入射粒子沉积速率的增大,薄膜表面的形貌逐步由少数聚集型岛核分布状态向众多各自独立的离散型岛核分布状态过渡. 进一步研究得出,薄膜覆盖度和入射粒子沉积速率对粒子扩散能力的影响最终导致岛的形貌发生了改变.