One-dimensional phase transitions in a two-dimensional optical lattice

A phase transition for bosonic atoms in a two-dimensional anisotropic optical lattice is considered. If the tunnelling rates in two directions are different, the system can undergo a transition between a two-dimensional superfluid and a one-dimensional Mott insulating array of strongly coupled tubes. The connection to other lattice models is exploited in order to better understand the phase transition. Critical properties are obtained using quantum Monte Carlo calculations. These critical properties are related to correlation properties of the bosons and a criterion for commensurate filling is established.     

Jamming percolation and glass transitions in lattice models

A new class of lattice gas models with trivial interactions but constrained dynamics is introduced. These models are proven to exhibit a dynamical glass transition: above a critical density rhoc ergodicity is broken due to the appearance of an infinite spanning cluster of jammed particles. The fraction of jammed particles is discontinuous at the transition, while in the unjammed phase dynamical correlation lengths and time scales diverge as exp[C(rhoc-rho)-mu]. Dynamic correlations display two-step relaxation similar to glass formers and jamming systems.     

广义布洛赫条件下二维晶格的磁交换作用

二维磁性材料是近几年新兴的研究领域,该材料在开发自旋电子器件等领域具备良好的应用潜能.为了了解二维磁性材料的磁性质,明确体系内各近邻磁性原子间的磁相互作用非常重要.第一性原理为各近邻磁交换参数的计算奠定了基础.目前各近邻参数的第一性原理计算常用的是能量映射法,但这种方法存在一定的缺陷.本文通过广义布洛赫条件推导了3种常见二维磁性结构的海森伯作用与Dzyaloshinskii-Moriya (DM)相互作用的自旋螺旋色散关系,这3种结构为四方结构,元胞包含一个磁性原子的六角结构,元胞包含两个磁性原子的六角结构.为了将本文推导的自旋螺旋色散关系应用于实际,我们通过第一性原理计算了一些材料的海森伯和DM作用的交换参数,这些材料分别是MnB,VSe₂,MnSTe,Cr₂I₃Cl₃.其中,MnSTe和Cr₂I3Cl₃都属于二维Janus材料,磁性原子层的上下层对称性破缺,整个体系存在DM相互作用.     

Thermal phase transitions at the percolation threshold

We present a simple argument, valid in all dimensions for a wide range of quenched dilute spin models, for the equality of the pair correlation function and the pair connectedness function at the point p = p_c, T = 0 is approached along the T axis.     

The geometrical phase transitions in a lattice model

We shall consider a finite range model on a square latticeZ ³ and show the existence of bubble, tubular and lamellar phases by estimating the correlation functions at low temperature.     

Isoperimetric phase transitions of two-dimensional droplets

We consider two-dimensional assemblies of particles governed by hamiltonians depending on the area and the perimeter of their convex hull. Provided the hamiltonian is quadratically homogeneous in the coordinates, we find an exact formula for the free energy. Phase transitions resulting from the competition between area and perimeter can easily be produced and explicitly dealt with. We illustrate those features by a simple example undergoing a second-order transition.     

Nonequilibrium phase transitions in a simple three-state lattice gas

We investigate the dynamics of a three-state stochastic lattice gas consisting of holes and two oppositely charged species of particles, under the influence of an electric field at zero total charge. Interacting only through an excluded-volume constraint, particles exchange with holes and, on a slower time scale, with each other. Using a combination of Monte Carlo simulations and meanfield equations of motion, we study a set of suitably defined order parameters, their histograms and fluctuations, as well as the current through the system. With increasing particle density and drive, the system first orders into a charge-segregated state, and then disorders again near complete filling. The transition is first order at low densities and turns second order at higher ones. The finite-size and aspect-ratio dependence of characteristic quantities is discussed at the mean-field level.     

Equilibration and dynamic phase transitions of a driven vortex lattice

We report on the observation of two types of current driven transitions in metastable vortex lattices. The metastable states, which are missed in usual slow transport measurements, are detected with a fast transport technique in the vortex lattice of undoped 2H-NbSe2. The transitions are seen by following the evolution of these states when driven by a current. At low currents we observe an equilibration transition from a metastable to a stable state, followed by a dynamic crystallization transition at high currents.     

Finite-temperature phase transitions in a two-dimensional boson Hubbard model

We study finite-temperature phase transitions in a two-dimensional boson Hubbard model with zero-point quantum fluctuations via Monte Carlo simulations of a quantum rotor model and construct the corresponding phase diagram. Compressibility shows a thermally activated gapped behavior in the insulating regime. Finite-size scaling of the superfluid stiffness clearly shows the nature of the Kosterlitz-Thouless transition. The transition temperature T(c) confirms a scaling relation T(c) proportional, rho(0)(x), with x=1.0. Some evidence of anomalous quantum behavior at low temperatures is presented.     

Continuous melting of a driven two-dimensional flux lattice with strong pins

The phase diagram of a driven two-dimensional vortex lattice in the presence of dense quasi-point pins is investigated. The transition from the crystal to the liquid is found continuous at intermediate inductions. The correlations in the pseudo random force that allow for an uncomplete unbinding of the dislocations is proposed as a key mechanism to account for the continuous transition.Received: 27 May 2003, Published online: 4 August 2003PACS: 64.60.Ht Dynamic critical phenomena - 74.60.Ge Flux pinning, flux creep and flux-line lattice dynamics     

Phase transitions in the two-dimensional antiferromagnetic Potts model on a triangular lattice

Phase transitions and thermodynamic properties in the two-dimensional three-state antiferromagnetic Potts model on a triangular lattice are investigated using the Monte Carlo method and the histogram analysis of the data. It is shown that pronounced first-order phase transitions are observed in this model for systems with rather large linear dimensions (L > 120). No first-order PTs are observed for systems with L < 120.     

Existence of phase transitions for quantum lattice systems

We prove that the following lattice systems:

1. anisotropic Heisenberg model,
2. Ising model with transverse magnetic field,
3. quantum lattice gas with hard cores extending over nearest neighbours,

exhibit phase transitions if the temperature is sufficiently low and the transverse (or kinetic) part of the interaction sufficiently small.     

Continuous quantum phase transition in a Kndo lattice model

We study the magnetic quantum phase transition in an anisotropic Kondo lattice model. The dynamical competition between the RKKY and Kondo interactions is treated using an extended dynamic mean field theory appropriate for both the antiferromagnetic and paramagnetic phases. A quantum Monte Carlo approach is used, which is able to reach very low temperatures, of the order of 1% of the bare Kondo scale. We find that the finite-temperature magnetic transition, which occurs for sufficiently large RKKY interactions, is first order. The extrapolated zero-temperature magnetic transition, on the other hand, is continuous and locally critical.     

First-order phase transitions in large entropy lattice models

We show the existence of a first-order phase transition in thev-dimensional Potts model forv≧2, when the number of states of a single spin is big enough. Low-temperature pure phases are proved to survive up to the critical temperature. Also the existence of a first-order transition in thev-dimensional Potts gauge model,v≧3, is obtained if the underlying gauge group is finite but large.     

Interactions and phase transitions on graphene's honeycomb lattice

The low-energy theory of interacting electrons on graphene's two-dimensional honeycomb lattice is derived and discussed. In particular, the Hubbard model in the large-N limit is shown to have a semimetal-antiferromagnetic insulator quantum critical point in the universality class of the Gross-Neveu model. The same equivalence is conjectured to hold in the physical case N=2, and its consequences for various physical quantities are examined. The effects of the long-range Coulomb interaction and the magnetic field are discussed.     

Dimerized phase and transitions in a spatially anisotropic square lattice antiferromagnet

We investigate the spatially anisotropic square lattice quantum antiferromagnet. The model describes isotropic spin-1/2 Heisenberg chains (exchange constant J) coupled antiferromagnetically in the transverse (J( perpendicular )) and diagonal (J(x)), with respect to the chain, directions. Classically, the model admits two ordered ground states-with antiferromagnetic and ferromagnetic interchain spin correlations-separated by a first-order phase transition at J( perpendicular )=2J(x). We show that in the quantum model this transition splits into two, revealing an intermediate quantum-disordered columnar dimer phase, both in two dimensions and in a simpler two-leg ladder version. We describe quantum-critical points separating this spontaneously dimerized phase from classical ones.