Spontaneous magnetization of the Ising model on a 4–8 lattice

The spontaneous magnetization of the Ising model on a 4–8 lattice with six different coupling constants and two different magnetic moments is studied. A formula for the spontaneous magnetization is proposed. The result agrees with the exact low-temperature series expansions up to the 12th order.     

Equilibrium polymerization in a solvent: Solution on the Bethe lattice

The lattice model for equilibrium polymerization in a solvent proposed by Wheeler and Pfeuty is solved exactly on a Bethe lattice (core of a Caylay tree) with general coordination numberq. Earlier mean-field results are reobtained in the limitq, but the phase diagrams show deviations from them for finiteq. Whenq=2, our results turn into the solution of the one-dimensional problem. Although the model is solved directly, without the use of the correspondence between the equilibrium polymerization model and the diluten0 model, we verified that the latter model may also be solved on the Bethe lattice, its solution being identical to the direct solution in all parameter space. As observed in earlier studies of the puren0 vector model, the free energy is not always convex. We obtain the region of negative susceptibility for our solution and compare this result with mean field and renormalization group (-expansion) calculations.     

Clusters,metastability, and nucleation: Kinetics of first-order phase transitions

We describe and interpret computer simulations of the time evolution of a binary alloy on a cubic lattice, with nearest neighbor interactions favoring like pairs of atoms. Initially the atoms are arranged at random; the time evolution proceeds by random interchanges of nearest neighbor pairs, using probabilities compatible with the equilibrium Gibbs distribution at temperatureT. For temperatures 0.59T_c, 0.81 T_c, and 0.89T _c, with density of A atoms equal to that in the B-rich phase at coexistence, the density C₁ of clusters ofl A atoms approximately satisfies the following empirical formulas: C₁ w(1 –)³ andC ₁, (1 –)⁴Q₁w¹ (2 l 10). Herew is a parameter and we defineQ _l = _K e ^–E(K) , where the sum goes over all translationally nonequivalentl-particle clusters andE(K) is the energy of formation of the clusterK. Forl > 10,Q ₁ is not known exactly; so we use an extrapolation formulaQ _l Aw _s ^–l l ^– exp(–bl ), wherew _s is the value ofw at coexistence. The same formula (withw > w _s) also fits the observed values of C, (for small values ofl) at densities greater than the coexistence density (forT=0.59T_c): When the supersaturation is small, the simulations show apparently metastable states, a theoretical estimate of whose lifetime is compatible with the observations. For higher supersaturation the system is observed to undergo a slow process of segregation into two coexisting phases (andw therefore changes slowly with time). These results may be interpreted as a more quantitative formulation (and confirmation) of ideas used in standard nucleation theory. No evidence for a spinodal transition is found.Supported by AFOSR Grant No. 73-2430D and by ERDA Contract No. EY-76-C-02-3077*000.     

High-density percolation: Exact solution on a Bethe lattice

A new percolation problem is posed where the sites on a lattice are randomly occupied but where only those occupied sites with at least a given numberm of occupied neighbors are included in the clusters. This problem, which has applications in magnetic and other systems, is solved exactly on a Bethe lattice. The classical percolation critical exponents=gg=1 are found. The percolation thresholds vary between the ordinary percolation thresholdp _c (m=1)=l/(z – 1) andp _c(m=z) =[l/(z – 1)]¹/(z–1). The cluster size distribution asymptotically decays exponentially withn, for largen, p p _c .Supported in part by National Science Foundation grant DMR78-10813.     

Phase transitions in lattice gas models for water

Water-like lattice gases on the triangular and body-centered cubic lattices are investigated. Molecules may reside on the lattice sites in either of two possible orientations, a hydrogen bond being formed between molecules on neighboring sites if they have the proper orientation with respect to one another. For a range of chemical potential at sufficiently low temperatures, the models are shown to have an ordered phase consisting of an open, hydrogen-bonded, icelike structure. The models are shown to be transitionfree at sufficiently high temperature, indicating the existence of a critical point.Research supported in part by the U.S. National Science Foundation, Grant CHE-7726177, and by The Robert A. Welch Foundation, Grant P-446.     

30CrMnSiNi2A晶格参量的测量及回复规律研究

针对X射线衍射领域中晶面衍射峰重叠问题,提出一种新的重叠峰分离方法.采用RU-200V转靶衍射仪对30CrMnSiNi2A晶格参量及其回复规律进行研究,得出不同回火温度下晶格参量与碳含量的变化关系.研究结果发现:由于碳的过饱和度不同以及合金元素的影响,30CrMnSiNi2A与高碳马氏体晶格参量的变化规律虽基本符合,但其变化速率存在差异.在不同回火温度下晶格参量a基本与碳含量无关,随着回火温度升高,a值略有下降.晶格参量c则随碳含量的变化幅度较大,从淬火态到180℃回火态出现一个陡降过程,随着回火温度升高,其变化幅度又趋于平缓.     

多目标最优化的一种积分型实现算法

在文[1]中给出了求解多目标最优化的一种积分总极值的概念性算法．本文利用数论中的一致分布佳点集列，较为简便的得出了多目标最优化的积分总极值的实现算法和算法终止准则．并经过有关函数数值计算表明该算法是有效的，可用来求解多目标最优化问题的有效解．     

密度矩阵重正化群的异构并行优化

密度矩阵重正化群方法（DMRG）在求解一维强关联格点模型的基态时可以获得较高的精度，在应用于二维或准二维问题时，要达到类似的精度通常需要较大的计算量与存储空间.本文提出一种新的DMRG异构并行策略，可以同时发挥计算机中央处理器（CPU）和图形处理器（GPU）的计算性能.针对最耗时的哈密顿量对角化部分，实现了数据的分布式存储，并且给出了CPU和GPU之间的负载平衡策略.以费米Hubbard模型为例，测试了异构并行程序在不同DMRG保留状态数下的运行表现，并给出了相应的性能基准.应用于4腿梯子时，观测到了高温超导中常见的电荷密度条纹，此时保留状态数达到10⁴，使用的GPU显存小于12 GB.     

X-ray photoemission spectra measurements of CeNi2Sb2 and CeCu2Sb2

X-ray photoemission spectra, resistivity and susceptibility of CeNi₂Sb₂ and CeCu₂Sb₂ were measured and are discussed. The results indicate that these alloys are Kondo systems. For comparison of the valence band properties, the spectra of the isostructural alloys of RT₂X₂-type with R = La, Gd, T = Cu, Ni and X = Sn, Sb were investigated, too.     

Extended Toda Lattice

We introduce nonlocal flows that commute with those of the classical Toda hierarchy. We define a logarithm of the difference Lax operator and use it to obtain a Lax representation of the new flows.