On the critical behavior of the magnetization in high-dimensional Ising models

We derive rigorously general results on the critical behavior of the magnetization in Ising models, as a function of the temperature and the external field. For the nearest-neighbor models it is shown that ind4 dimensions the magnetization is continuous atT _c and its critical exponents take the classical values=3 and=1/2, with possible logarithmic corrections atd=4. The continuity, and other explicit bounds, formally extend tod>3 1/2. Other systems to which the results apply include long-range models ind=1 dimension, with 1/|x–y| couplings, for which 2/(–1) replacesd in the above summary. The results are obtained by means of differential inequalities derived here using the random current representation, which is discussed in detail for the case of a nonvanishing magnetic field.Research supported in part by NSF grant PHY-8301493 A02, and by a John S. Guggenheim Foundation fellowship (M.A.).     

Monte Carlo simulation of three-dimensional dilute Ising model

A multispin coding program for site-diluted Ising models on large simple cubic lattices is described in detail. The spontaneous magnetization is computed as a function of temperature, and the critical temperature as a function of concentration is found to agree well with the data of Marro et al.⁽⁴⁾ and Landau⁽³⁾ for smaller systems.The first successful epsilon expansion seems to be by D. E. Khmelnitskii,ZhETF 68:1960 (1975), English translationSov. Phys. JETP 41:981 (1975); for numerical estimates see K. E. Newman and E. K. Riedel,Phys. Rev. H25:264 (1982), for experiments see R. J. Birgenau, R. A. Cowley, G. Shirane and H. Yoshizawa,J. Stat. Phys. 34:817 (1984).     

Critical behavior of the two-dimensional first passage time

We study the two-dimensional first passage problem in which bonds have zero and unit passage times with probabilityp and 1–p, respectively. We prove that as the zero-time bonds approach the percolation thresholdp _c, the first passage time exhibits the same critical behavior as the correlation function of the underlying percolation problem. In particular, if the correlation length obeys(p) ¦p–p _c¦^–v, then the first passage time constant satisfies(p)¦p–p _c¦^v. At p_c, where it has been asserted that the first passage time from 0 tox scales as ¦x¦ to a power with 0<<1, we show that the passage times grow like log ¦x¦, i.e., the fluid spreads exponentially rapidly.     

A branching process model for sand avalanches

An analytically solvable model for sand avalanches of noninteracting grains of sand, based on the Chapman-Kolmogorov equations, is presented. For a single avalanche, distributions of lifetimes, sizes of overflows and avalanches, and correlation functions are calculated. Some of these are exponentials, some are power laws. Spatially homogeneous distributions of avalanches are also studied. Computer simulations of avalanches of interacting grains of sand are compared to the solutions to the Chapman-Kolmogorov equations. We find that within the range of parameters explored in the simulation, the approximation of noninteracting grains of sand is a good one.     

Study of the three-dimensional Ising model on film geometry with the cluster Monte Carlo method

Topological properties of clusters are used to extract critical parameters. This method is tested for the bulk properties ofd=2 percolation and thed=2, 3 Ising model. For the latter we obtain an accurate value of the critical temperatureJ/k _B T _c=0.221617(18). In the case of thed=3 Ising model with film geometry the critical value of the surface coupling at the special transitions is determined as J_1c/J=1.5004(20) together with the critical exponents ₁ ^m =0.237(5) and=0.461(15).     

集中荷载下叠合梁抗剪强度

本文对低叠合面钢筋破简支在合梁二阶段受力的斜截面抗剪性能进行了试验研究，并运用非线性有限元分析和试验实测数据，得出了一个适合于集中荷载下高低叠合面叠合梁的抗剪强度计算公式．     

不同负荷下餐厨垃圾与水稻秸秆共消化厌氧产氢研究

进料负荷对餐厨垃圾与水稻秸秆混合厌氧发酵产氢过程有重要影响. 以进料负荷为影响因子, 设置温度均为55℃的餐厨垃圾与水稻秸秆混合厌氧发酵产氢实验, 其中进料负荷(以VS计)分别设置为(A)5kg?m-3?d-1、(B)10kg?m-3?d-1、(C)15kg?m-3?d-1, 分析厌氧产氢过程中产气量、产氢速率、pH、VFAs、氨氮、SCOD等参数的变化. 实验结果表明: B组发酵底物产气量最大, 为8664mL, 产氢速率也最大, 为748.3mL?h-1, 反应过程中pH始终维持在5.5±0.1内, 是厌氧产氢的最佳范围. 实验结束时, 各组VFAs、氨氮浓度分别为7292.46、8248.35、8558.24mg?L-1和544.48、754.31、1458.33mg?L-1. 同时各组SCOD浓度变化趋势相似. 在研究范围的最佳进料负荷下, 进行回流比分别为10%、30%、50%的实验, 结果显示30%回流比的产氢量最大, 为56039mL, 同时运行过程中系统稳定性较好. 综上所述, 进料负荷为10kg?m-3?d-1, 30%回流比的餐厨垃圾与水稻秸秆混合厌氧发酵产氢时, 微生物活性较好, 能够产生更多的氢气. 这一结果可为餐厨垃圾资源化提供参考依据.     

A new comprehensive study of the 3D random-field Ising model via sampling the density of states in dominant energy subspaces

The three-dimensional bimodal random-field Ising model is studied via a new finite temperature numerical approach. The methods of Wang-Landau sampling and broad histogram are implemented in a unified algorithm by using the N-fold version of the Wang-Landau algorithm. The simulations are performed in dominant energy subspaces, determined by the recently developed critical minimum energy subspace technique. The random-fields are obtained from a bimodal distribution, that is we consider the discrete (±Δ) case and the model is studied on cubic lattices with sizes 4≤L ≤20. In order to extract information for the relevant probability distributions of the specific heat and susceptibility peaks, large samples of random-field realizations are generated. The general aspects of the model's scaling behavior are discussed and the process of averaging finite-size anomalies in random systems is re-examined under the prism of the lack of self-averaging of the specific heat and susceptibility of the model.     

对《二维六角形晶格伊辛模型的重正化群解》一文的进一步计算

针对《二维六角形晶格伊辛模型的重正化群解》一文中有关〈V〉0的计算进行了修正,给出了新的重正化群的变换、重正化群的线性化变换矩阵以及临界指数.     

Effect of exchange interaction in ferromagnetic superlattices:A Monte Carlo study

The Monte Carlo simulation is used to investigate the magnetic properties of ferromagnetic superlattices through the Ising model. The reduced critical temperatures of the ferromagnetic superlattices are studied each as a function of layer thickness for different values of exchange interaction. The exchange interaction in each layer within the interface and the crystal field in the unit cell are studied. The magnetic coercive fields and magnetization remnants are obtained for different values of exchange interaction, different values of temperature and crystal field with fixed values of physical parameters.