Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions

We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar–Parisi–Zhang universality class of critical behavior. We remark that a whole family of RSOS interface models similar to the Ising interface model investigated here can be described by exactly solvable restricted high-spin quantum XXZ$XXZ$-type Hamiltonians.     

Mass generations in two-dimensional hierarchical Heisenberg model of Migdal-Kadanoff type

Finiteness of correlation length in the 2D Heisenberg model is established within the Migdal-Kadanoff approximate renormalization recursion formulas.     

Observation of two-dimensional lattice interface solitons

We report on the experimental observation of two-dimensional solitons at the interface between square and hexagonal waveguide arrays. In addition to the different symmetries of the lattices, the influence of a varying refractive index modulation depth is investigated. Such variation strongly affects the properties of surface solitons residing at different sides of the interface.     

Renormalization group flow of two-dimensional hierarchical Heisenberg model of Dyson-Wilson type

Two-dimensionalO(N)-invariant hierarchical Heisenberg models (of Dyson-Wilson type) are investigated by the real space renormalization group method. It is established that ifN2, then the effective actions at long distance scales are driven into the high temperature region by the iterative use of the block spin transformations thus concluding the non-existence of phase transitions in the system. The correlation functions are also obtained and they decay at the speed of massive gaussian field model. The driving force is geometrical and an a priori one and stronger than the boundary effect which is bounded byO(1) in the present system. Thus the hierarchical formulas fail to exhibit the Kosterlitz-Thouless transitions (at least forN=2).     

Deconfinement in the two-dimensional XY model

The unbinding of vortex-antivortex pairs for the classical two-dimensional XY model in a magnetic field is studied. A single such pair is connected by a string of overturned spins, leading to linear confinement. We show that this system supports two phase transitions, one in which closed strings proliferate, and a second in which vortices unbind. The transitions are shown to be dual to one another, and are remarkably continuous. Possible consequences for a variety of systems are discussed.     

Superconductivity in the two-dimensional t-J model

Using computational techniques, it is shown that pairing is a robust property of hole-doped antiferromagnetic insulators. In one dimension and for two-leg ladder systems, a BCS-like variational wave function with long-bond spin singlets and a Jastrow factor provides an accurate representation of the ground state of the t-J model, even though strong quantum fluctuations destroy the off-diagonal superconducting long-range order in this case. However, in two dimensions it is argued-and numerically confirmed using several techniques, especially quantum Monte Carlo-that quantum fluctuations are not strong enough to suppress superconductivity.     

Metastability in the two-dimensional ising model

Metastability in the Ising model is studied in two ways. In a dynamical Monte Carlo model, metastable magnetization and lifetime are measured for various magnetic fields and low temperatures. Following up a proposed relation between analytic continuation of transfer matrix eigenvalues and metastability, transfer matrix eigenvalues are studied. We examine the extent to which these approaches agree. The Monte Carlo data also provide quantitative support for the critical droplet model for decay.     

Exact treatment of interface fluctuations in a two-dimensional emulsion

Summary We present a model for a polydisperse ensemble of two-dimensional droplets wich accounts for the effects of arbitrarily large distortions of the droplet shape. Interactions within a droplet include bending rigidity and spontaneous curvature. Interactions between droplets are omitted. Even at high temperatures, the effects of the shape fluctuations on the droplet size distribution remain small, as they are dominated by the contributions from the mixing entropy. In contrast, shape fluctuations lead to a pronounced peak in thermodynamic quantities like specific heat. This peak occurs at temperatures where thermal excitations become of the order of the bending energies of the droplet surface. The fluctuation-dominated regime extends to temperatures far lower than expected from a mean-field calculation. Paper presented at the I International Conference on Scaling, Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

二维声子晶体中Zak相位诱导的界面态

界面态具有巨大的实际应用价值,因此寻找界面态是一个既有科学意义也有应用前景的课题.在本文中,我们通过把二维正方晶格声子晶体的结构单元进行倾斜,构造出具有线性狄拉克色散的斜方晶格体系.狄拉克色散引起体能带Zak相位的π跃变,使得位于狄拉克锥投影能带两边的带隙具有不同符号的表面阻抗,从而导致由正方晶体体系与由其“倾斜”的斜方晶格体系构成的界面处存在确定性的界面态.     

Corner exponents in the two-dimensional Potts model

The critical behavior at a corner in two-dimensional Ising and three-state Potts models is studied numerically on the square lattice using transfer operator techniques. The local critical exponents for the magnetization and the energy density for various opening angles are deduced from finite-size scaling results at the critical point for isotropic or anisotropic couplings. The scaling dimensions compare quite well with the values expected from conformal invariance, provided the opening angle is replaced by an effective one in anisotropic systems.     

Stripe phases in the two-dimensional Falicov-Kimball model

The observation of charge stripe order in the doped nickelate and cuprate materials has motivated much theoretical effort to understand the underlying mechanism of the stripe phase. Numerical studies of the Hubbard model show two possibilities: (i) stripe order arises from a tendency toward phase separation and its competition with the long-range Coulomb interaction or (ii) stripe order inherently arises as a compromise between itinerancy and magnetic interactions. Here we determine the restricted phase diagram of the two-dimensional Falicov-Kimball model and see that it displays rich behavior illustrating both possibilities in different regions.     

二维伊辛模型的畴壁动力学

表面可以改变纳米磁性薄膜的结构和相变温度,畴壁动力学由此成为研究的重点.本文采用动力学蒙特卡罗模拟方法,对二维Ising模型磁畴界面的非平衡动力学展开数值研究.系统初态设为半正半负,即由完全有序但自旋取向完全相反的两部分组成,其间的磁畴壁随时间生长.通过对磁化标度形式的分析,发现畴壁内外的动力学标度形式虽然相同,但临界...