嵌套正方格子上反铁磁高斯模型的相变

采用等效变换的方法,把嵌套正方晶格转化为可求解的正方晶格.利用重整化群变换,我们求得了正方系统的临界点.结合本文中给出的两个变换关系,得到了嵌套正方晶格上反铁磁高斯模型的临界点为K*=-0.707b.     

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.     

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.     

镶嵌正方晶格上Gauss模型的相图

利用等效变换和自旋重标相结合的方法, 研究了镶嵌正方晶格上的Gauss模型. 研究 发现, 该系统可以变换为正方晶格上具有最近邻和次近邻相互作用的Gauss系统, 由此严格求得了镶嵌正方晶格上Gauss模型的临界温度, 得到了该系统的精确相图.     

Union Jack晶格上伊辛模型的自由费密近似解

运用自由费密近似对Union Jack晶格上具有各向异性二体耦合作用及三体相互作用的伊辛模型进行了求解,得到了模型的自由能、自发磁矩和临界点方程。在耦合常数简化为正方晶格上的伊辛模型时,得到了与Onsager一致的解。     

具有Dzyaloshinskii-Moriya作用的Blume-Capel模型的临界性质

应用二自旋集团平均场近似的方法,研究了蜂窝晶格和正方晶格上具有Dzyaloshinskii-Moriya(DM)作用的Blume-Capel模型的临界性质,得到了该系统的相图。结果表明,所研究系统存在三临界点,并且三临界温度不随DM作用参量单调变化,三临界温度有最小值。系统的这种临界性质是交换耦合作用、晶体场作用和DM作用三者相互竞争的结果。     

长程作用下Gauss系统的临界温度

利用傅里叶变换的方法，严格求解了d维(d=1，2和3)超立方晶格和二维三角晶格上具有长程 相互作用的Gauss模型(这里考虑的长程作用有幂指数、指数和对数三种形式).得到了这些情 况下系统的临界点(温度)，并对不同形式的长程作用对临界点的影响进行了比较.结果表明 ，长程相互作用的存在，使得系统的临界温度有了一定程度的升高，它们对系统临界温度的 影响与其衰减的快慢有关. 关键词： Gauss模型 临界点 超立方晶格 三角晶格     

不同结构光子晶体的带隙特性

基于平面波展开法研究光子晶体的带隙特性,数值模拟了横磁波和横电波在三角晶格和正方晶格构成的二维光子晶体中的带隙特性,得到了三角晶格较正方晶格更容易出现带隙,且三角晶格的横电波光子带隙较大.实验结果为光子晶体器件的设计提供理论依据.     

大粒子数二维硬核玻色子系统的量子蒙特卡罗模拟

采用随机级数展开的量子蒙特卡罗方法研究二维硬核的玻色-赫伯德模型的热力学性质. 首先通过算符变换将模型映射成为二维反铁磁准海森伯模型. 变换后的模型比通常的海森伯模型多一项, 该项正比于系统的格点总数 N, 对于大粒子数的系统, 该项使模拟耗时指数增加, 所以难以计算大粒子数系统.采用非局域操作循环更新后, 这个困难可以得到很好的解决, 可使粒子数总数增大到几千个.研究结果表明, 粒子数密度在0-0.5范围内增大时, 能量呈递减趋势, 并趋于某一定值, 随着正方晶格系统尺度增大, 能量也随之增大;正方晶格系统尺度一定时, 能量和磁化强度随着温度的升高而增大, 化学势的变化对能量和磁化强度没有影响, 能量随着正方晶格系统尺度增大而增大, 磁化强度却随之减小;正方晶格系统尺度一定时, 化学势的增大对比热没有影响, 随着温度的升高比热出现先增大后减小的趋势, 最后趋于某个值, 达到平衡, 而正方晶格系统尺度越大, 比热曲线增大部分的趋势越大, 减小部分的趋势也更明显, 参照朗道超流理论, 本文模拟的能量和比热曲线趋势与朗道二流体模型下He II的理论研究一致; 不同正方晶格系统尺度的影响不大, 均匀磁化率倒数在0-0.5(J/k_B)的低温范围内有很小的波动, J为耦合能, k_B为玻尔兹曼常数, 温度在0.5-2 (J/k_B)的范围内, 均匀磁化率的倒数随着温度的升高而增大, 且曲线的趋势显示了一种类似近藤行为.     

用转移矩阵法数值研究二维正方介质柱光子晶体的传输特性

利用转移矩阵方法对二维正方介质柱光子晶体的传输特性进行了研究,数值计算研究了不同晶格、同一晶格柱体截面面积不同、放置方位角不同时光子晶体的传输特性。数值结果表明光子禁带的宽度与中心频率和晶格结构有很大关系,正方晶格更易形成平坦光子禁带,柱体截面面积大,则形成的禁带较宽,在其他因素相同的条件下柱体放置的方位角对光子禁带有重要影响。数值研究表明在正方介质柱下设计宽平坦光子禁带时,可以首先考虑正方晶格结构,其次设法使柱体截面尽量大一些,最后可通过柱体放置方位角来微调光子禁带的宽度与中心频率以达到设计要求。     

A Solvable Decorated Ising Lattice Model

A decorated lattice is suggested and the Ising model on it with three kinds of interactions K₁, K₂, and K₃ is studied. Using an equivalent transformation, the square decorated Ising lattice is transformed into a regular square Ising lattice with nearest-neighbor, next-nearest-neighbor, and four-spin interactions, and the critical fixed point is found at K₁=0.5769, K₂=-0.0671, and K₃=0.3428, which determines the critical temperature of the system. It is also found that this system and the regular square Ising lattice, and the eight-vertex model belong to the same universality class.     

一个镶嵌稀释双键Potts模型的严格解

本文研究在一个镶嵌正方形格子上的一个稀释双键Potts模型,模型中既包含铁磁作用,也包含反铁磁作用。得到了非常一般的和某些特殊情况下的临界行为的严格解及相图。特别是,我们的结果中展示出在二维情况下,当q≤3时,稀释反铁磁Potts模型也如同正规(非稀释)模型一样,存在着特殊的低温相。 关键词：     

Absence of a spontaneous long-range order in a mixed spin-(1/2, 3/2) Ising model on a decorated square lattice due to anomalous spin frustration driven by a magnetoelastic coupling

The mixed spin-(1/2, 3/2) Ising model on a decorated square lattice, which takes into account lattice vibrations of the spin-3/2 decorating magnetic ions at a quantum-mechanical level under the assumption of a perfect lattice rigidity of the spin-1/2 nodal magnetic ions, is examined via an exact mapping correspondence with the effective spin-1/2 Ising model on a square lattice. Although the considered magnetic structure is in principle unfrustrated due to bipartite nature of a decorated square lattice, the model under investigation may display anomalous spin frustration driven by a magnetoelastic coupling. It turns out that the magnetoelastic coupling is a primary cause for existence of the frustrated antiferromagnetic phases, which exhibit a peculiar coexistence of antiferromagnetic long-range order of the nodal spins with a partial disorder of the decorating spins with possible reentrant critical behavior. Under certain conditions, the anomalous spin frustration caused by the magnetoelastic coupling is responsible for unprecedented absence of spontaneous long-range order in the mixed-spin Ising model composed from half-odd-integer spins only.     

Physical realization and possible identification of topological excitations in quantum Heisenberg anti-ferromagnet on a two dimensional lattice

Physical spin configurations corresponding to topological excitations, expected to be present in the XY limit of a quantum spin 1/2 Heisenberg anti-ferromagnet, are probed on a two dimensional square lattice. Quantum vortices (anti-vortices) are constructed in terms of coherent staggered spin field components, as limiting case of meronic (anti-meronic) configurations. The crucial role of the associated Wess-Zumino-like (WZ-like) term is highlighted in our procedure. The time evolution equation of coherent spin fields used in this analysis is obtained by applying variational principle on the quantum Euclidean action corresponding to the Heisenberg anti-ferromagnet on lattice. It is shown that the WZ-like term can distinguish between vortices and anti-vortices only in a charge sector with odd topological charges. Our formalism is distinctly different from the conventional approach for the construction of quantum vortices (anti-vortices).     

Exact results for a dilute Potts model

Exact results are obtained for the annealed, dilute,q-component Potts model on the decorated square lattice. The phase diagram is found to consist of a high-temperature region, a low-temperature region, and a two-phase region in between which arises only forq>4: exact expressions for the phase boundary and the critical probability are derived. At the critical point the specific heat is generally finite and has a cusp; the slope of the cusp is finite forq=4 and infinite (vertical) forq=2 and 3.Work supported in part by NSF Grant No. DMR 78-18808.     

The critical line of an asymmetric eight vertex model

Phenomenological renormalization of finite lattice data is used to locate the critical line of an asymmetric eight-vertex model. This model reduces at a special point to a loop gas on the square lattice. The critical fugacity of the loop gas is estimated to be 2.373±0.001, whereas the correlation exponent appears to be Ising-like.     

Decorated ising model with classical vector spins

A decorated Ising model with classical vector spins on a square lattice is investigated in detail. The partition function is reduced to the one of the Ising model with effective exchange integrals. Three successive phase-transition temperatures are obtained and four states, namely, paramagnetic, antiferromagnetic, again paramagnetic and ferromagnetic states are realized as the temperature is decreased. For systems on other two- and three-dimensional loose-packed lattices, the situation is the same as the system on the square lattice.