X分形晶格上Gauss模型的临界性质

采用实空间重整化群变换的方法,研究了2维和d(d>2)维X分形晶格上Gauss模型的临界性质.结果表明:这种晶格与其他分形晶格一样,在临界点处,其最近邻相互作用参量也可以表示为K=bqiqi(qi是格点i的配位数,bqi是格点i上自旋取值的Gauss分布常数)的形式;其关联长度临界指数v与空间维数d(或分形维数df)有关.这与Ising模型的结果存在很大的差异. 关键词： X分形晶格 重整化群 Gauss模型 临界性质     

随机外磁场对一维Blume-Capel模型动力学性质的影响

近几十年来,量子自旋系统的动力学性质引起了人们的广泛关注,随着研究的不断深入,随机自旋系统的性质受到了人们的重视. 利用递推关系式方法研究了高温极限下随机外磁场中自旋s=1的一维Blume-Capel模型的动力学性质, 通过计算自旋自关联函数和相应的谱密度,探讨了外场对系统动力学行为的影响.研究表明,在无晶格场的情况下, 当外场满足双模分布时,系统的动力学性质存在从中心峰值行为到集体模行为的交跨效应.当外场满足Gauss分布, 标准偏差较小时,系统也存在交跨效应;标准偏差足够大时,系统只表现为无序行为. 另外还研究了晶格场对系统动力学性质的影响,发现晶格场的存在减弱了系统的集体模行为.     

镶嵌正方晶格上具有次近邻耦合作用Ising模型的临界性质

采用部分格点自旋消约变换,将镶嵌正方晶格上具有最近邻耦合作用K1和次近邻耦合作用K2的Ising模型变换成等效的具有最近邻、次近邻和四体耦合作用的正方Ising晶格.发现系统的临界点在(K1C,K2C)=(0.5125,0.2134),由此决定系统的临界温度,幷讨论了系统的普适性.     

三模型随机场对一维量子Ising模型动力学性质的调控

量子自旋系统在外磁场下的动力学性质一直是凝聚态理论和统计物理研究的热点.本文利用递推关系方法,通过计算系统的自旋关联函数及其对应的谱密度,研究了三模型随机外场对一维量子Ising模型动力学性质的调控效应.在三模型随机横场下,利用r分支引入了非磁性杂质,研究表明:非磁性杂质使得系统的低频响应得到保持,中心峰值行为更加明显;非磁性杂质与横场之间的竞争能激发出新的频率响应,呈现多峰行为;但较多的非磁性杂质最终会限制系统对横场的响应.此外,研究还发现随机横场的三模分布参数满足qB_q=pB_p这一条件,是使中心峰值行为得到保持的有利条件.在三模型随机纵场下, r分支仅仅起到调节纵场强度的作用,且r分支所占比重的增大不利于低频响应,与三模型随机横场下r分支的调控作用是相反的.     

三维Ising模型矩阵解法的简化与近似解

利用Ising模型在无外场周期边界条件下的哈密顿量的对称性,对矩阵进行块对角化,严格求得2×2×n简单立方晶格Ising模型的解析解,对其他两种自旋集团较小的情况的热力学函数自由能进行数值计算,在数据拟合的基础上提出一种近似解. 关键词：     

镶嵌正方晶格上Ising模型的近似解

采用格点自旋消约方法,将具有最近邻和次近邻耦合作用的镶嵌正方Ising晶格变换成等效的具有最近邻、次近邻和四体耦合作用的正方Ising晶格,得到系统近似解的临界点在K′C=0.4406868.结果表明:在相变点最近邻耦合作用K1和次近邻耦合作用K2之间满足一定关系.如果只计及镶嵌正方Ising晶格的最近邻耦合作用K1,则其严格解的临界点在K1C=0.7635.由此可以推断在正方格点间安放两个自旋的双镶嵌正方Ising晶格,在只计及最近邻耦合作用情况下,也是严格可解的.     

蜂窝状格子带有晶场作用的铁磁Ising混合自旋S=1和S=1/2的相图的Monte-Carlo研究

利用具有翻转单个自旋的Metropolis-Monte-Carlo算法,研究蜂窝状格子带有晶场作用的铁磁Ising混合自旋S=1和S=1/2的相图,所得相图与严格解相接近,好于关联有效场方法得出的结果。因此Metropolis-Monte-Carlo算法同样也可以用于研究混合自旋模型。     

相变与临界现象(Ⅱ)——Ising模型

Ising模型是磁性系统的一个粗糙模拟。在正规晶格的每个格点位置上放一个“经典”的自旋,自旋方向可以向上或向下,习惯上我们用一个变量σ来表示自旋,σ可取±1。两个自旋σ_1和σ_2之间的相互作用能为-Jσ_1σ_2。当J>0时,所有自旋都指向同一方向的位形,在能量上最低,我们称这个系统为铁磁性的。一维模型是Ising于1925年解决的,二维模型首先是Onsager于1944年所解,而三维模型至今未解出。 为了说明问题的复杂性,我们先自一维系统着手,然后再推导二维模型的解。     

随机纵场对一维量子Ising模型动力学性质的影响

量子自旋系统的动力学性质是统计物理和凝聚态理论研究的热点问题.本文利用递推关系方法,通过计算系统的自旋关联函数及谱密度,研究了纵场对一维量子Ising模型动力学性质的影响.对于常数纵场的情况,发现当自旋耦合相互作用较弱时纵场能够引起不同动力学行为之间的交跨效应,且驱使系统出现了多种振动模式,但较强的自旋耦合相互作用会掩盖纵场的影响.对于随机纵场的情况,分别讨论了双模型随机纵场和高斯型随机纵场的影响,发现不同随机类型下的动力学结果有很大的差别,且高度依赖于随机分布中参数的选取,如双模分布的均值,高斯分布的均值和偏差等.尽管常数纵场和随机纵场下的动力学结果不同,但可以得到一个共同的结论:当纵场所占比重较大时,系统的中心峰值行为将得到保持.且此结论可以推广:系统哈密顿中非对易项的出现有利于中心峰值行为的保持.     

横向随机晶场Ising模型的相图和磁化行为研究

在有效场理论和切断近似框架内，选择自旋S=1的二维方格子，研究横向随机晶场Ising模型的相图和磁化行为，重点是横向随机晶场浓度和晶场比率对相图和磁化的影响.给出了i>T-D_x空间的相图和m-T空间的磁化图.在晶场稀疏情况下，负晶场方向存在临界温度的峰值，正方向可出现重入现象.晶场比率取+0.5和-0.5时，磁有序相范围缩小，特别是晶场比率取-0.5时，随晶场浓度的降低，临界温度峰值从横向晶场负方向渡越到正方向.固定某一负晶场值，不同晶场比率的磁化行为有明显差异.同时与纵向稀疏晶场Ising模型结果进行有意义的比较. 关键词： 横向随机晶场Ising模型 相图 磁化行为     

The Ising Susceptibility Scaling Function

We have dramatically extended the zero field susceptibility series at both high and low temperature of the Ising model on the triangular and honeycomb lattices, and used these data and newly available further terms for the square lattice to calculate a number of terms in the scaling function expansion around both the ferromagnetic and, for the square and honeycomb lattices, the antiferromagnetic critical point.     

一簇金刚石晶格上S~4模型的相变

采用重整化群和累积展开的方法,研究了一簇金刚石晶格上S~4模型的相变,求得了系统的临界点.结果表明:当分支数m=2和m 12时,该系统只存在一个Gauss不动点K~*=b_2/2, u_2~*=0;当分支数3≤m≤12时,该系统不仅有Gauss不动点,还存在一个Wilson-Fisher不动点,并且后一个不动点对系统的临界特性产生决定性的影响.     

Density of the Fisher Zeroes for the Ising Model

The density of the Fisher zeroes, or zeroes of the partition function in the complex temperature plane, is determined for the Ising model in zero field as well as in a pure imaginary field i/2. Results are given for the simple-quartic, triangular, honeycomb, and the kagomé lattices. It is found that the density diverges logarithmically at points along its loci in appropriate variables.     

Critical Behavior of Gaussian Model on X Fractal Lattices in External Magnetic Fields

Using the renormalization group method, the critical behavior of Gaussian model is studied in external magnetic fields on X fractal lattices embedded in two-dimensional and d-dimensional (d ＞ 2) Euclidean spaces, respectively. Critical points and exponents are calculated. It is found that there is long-range order at finite temperature for this model, and that the critical points do not change with the space dimensionality d (or the fractal dimensionality dr). It is also found that the critical exponents are very different from results of Ising model on the same lattices, and that the exponents on X lattices are different from the exact results on translationally symmetric lattices.     

Partition function zeros for the two-dimensional Ising model

The distribution of complex temperature zeros of the partition function of the two-dimensional Ising model in the absence of a magnetic field is investigated. For anisotropic square and triangular lattices the distribution function is two-dimensional and satisfies a partial differential equation derived from a generalized scaling theory. Corresponding results for the isotropic square, triangular and honeycomb lattices are also presented.     

Replica symmetry breaking in the Ising spin glass model on Bethe-like lattices with loop

The Ising spin glass model on Bethe-like lattices (cactus lattices) is studied using replicas in the presence of a magnetic field. Parisi's order parameter function and the de Almeida–Thouless (AT) line are obtained close to the spin glass transition temperature. The results are compared with those for the Bethe lattice to see the effects of loops. The slope of the order parameter function diminishes considerably for both lattices compared with that for the Sherrington–Kirkpatrick (SK) model. The loci of the AT line for the cactus lattices and the Bethe lattice are above and below that for the SK model, respectively.     

Comparison of diluted antiferromagnetic Ising models on frustrated lattices in a magnetic field

We study diluted antiferromagnetic Ising models on triangular and kagome lattices in a magnetic field, using the replica-exchange Monte Carlo method. We observe seven and five plateaus in the magnetization curve of the diluted antiferromagnetic Ising model on the triangular and kagome lattices, respectively, when a magnetic field is applied. These observations contrast with the two plateaus observed in the pure model. The origin of multiple plateaus is investigated by considering the spin configuration of triangles in the diluted models. We compare these results with those of a diluted antiferromagnetic Ising model on the three-dimensional pyrochlore lattice in a magnetic field pointing in the [111] direction, sometimes referred to as the “kagome-ice” problem. We discuss the similarity and dissimilarity of the magnetization curves of the “kagome-ice” state and the two-dimensional kagome lattice.     

Phase Diagram and Tricritical Behavior of a Spin-2 Transverse Ising Model in a Random Field

The phase diagrams of a spin-2 transverse Ising model with a random field on honeycomb, square, and simple-cubic lattices, respectively, are investigated within the framework of an effective-field theory with correlations.We find the behavior of the tricritical point and the reentrant phenomenon for the system with any coordination number z, when the applied random field is bimodal. The behavior of the tricritical point is also examined as a function of applied transverse field. The reentrant phenomenon comes from the competition between the transverse field and the random field.     

Multifractal magnetization on hierarchical lattices

A new approach is applied to show that the local magnetization of the ferromagnetic Ising model on hierarchical lattices has a multifractal structure at the critical point. Thef() function characterizing its multifractality is presented and discussed for the diamond hierarchical lattice. Distinct exact critical exponents for the average magnetization and for the local magnetization of the deepest sites are found. The average magnetization (as function of the temperature) is also calculated. The critical exponent of the susceptibility is estimated using finite-size scale arguments.