Weak disorder in a two-dimensional dipole magnet

The effect of “random-field” disorder and “random-anisotropy-axis” disorder on a two-dimensional dipole ferromagnet is investigated. It is shown that disorder results in instability of the ferromagnetic phase. The correlation function of the magnetization is calculated with the aid of a self-consistent harmonic approximation. It is found that in the presence of a random field the correlation function is a power-law function of the distance. In the presence of random anisotropy the correlation function decreases logarithmically slowly as a function of distance. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 108–112 (10 January 1997)     

Quantum percolation in two-dimensional antiferromagnets

The interplay of geometric randomness and strong quantum fluctuations is an exciting topic in quantum many-body physics, leading to the emergence of novel quantum phases in strongly correlated electron systems. Recent investigations have focused on the case of homogeneous site and bond dilution in the quantum antiferromagnet on the square lattice, reporting a classical geometric percolation transition between magnetic order and disorder. In this study we show how inhomogeneous bond dilution leads to percolative quantum phase transitions, which we have studied extensively by quantum Monte Carlo simulations. Quantum percolation introduces a new class of two-dimensional spin liquids, characterized by an infinite percolating network with vanishing antiferromagnetic order parameter.     

Disordered magnet near the percolation threshold

A disordered Potts magnet containing a random mixture of ferromagnetic exchange constants J_a and J_b (J_a?J_b) near the percolation threshold is considered. The scaling form for the free energy contains two crossover exponents. Duality arguments in two dimensions show that these exponents are equal. They are also shown to be equal to unity in d = 6 ? ? dimensions to order ?.     

Ordering in two-dimensional β-alumina structures

Elementary theoretical approaches to the ordering of the mobile ions in the conduction plane of β-alumina and β″ alumina predict a first order phase transition. Such transitions are not seen in experiments. Inhomogeneity and/or two-dimensionality may explain the difference between theory and experiment.     

Transport and percolation in a low-density high-mobility two-dimensional hole system

We present a study of the temperature and density dependence of the resistivity of an extremely high quality two-dimensional hole system grown on the (100) surface of GaAs. For high densities in the metallic regime (p > or approximately4x10;{9} cm;{-2}), the nonmonotonic temperature dependence ( approximately 50-300 mK) of the resistivity is consistent with temperature dependent screening of residual impurities. At a fixed temperature of T=50 mK, the conductivity versus density data indicate an inhomogeneity driven percolation-type transition to an insulating state at a critical density of 3.8x10;{9} cm;{-2}.     

Channeling and percolation in two-dimensional chaotic dynamics

The Hamiltonian dynamics of a particle moving in a nearly periodic two-dimensional (2-D) potential of square symmetry is analyzed. The particle undergoes two types of unbounded stochastic or random walks in such a system: a quasi-1-D motion (a "stochastic channeling") and a 2-D motion which results from a sort of stochastic percolation. A scenario for the onset of this stochastic percolation is analyzed. The threshold energy for percolation is found as a function of the perturbation parameter. Each type of random walk has the property of intermittency. The particle transport is anomalous in certain energy intervals.     

Ordering kinetics in quasi-one-dimensional Ising-like systems

We present results of a Monte Carlo simulation of the kinetics of ordering in the two-dimensional nearest-neighbor Ising model in anL xM geometry with two free boundaries of length ML. This model can be viewed as representing an adsorbant on a stepped surface with mean terrace widthL. We follow the ordering kinetics after quenches to temperatures 0.25 T/T_c 1 starting from a random initial configuration at a coverage of=0.5 in the corresponding lattice gas picture. The systems evolve in time according to a Glauber kinetics with nonconserved order parameter. The equilibrium structure is given by a one-dimensional sequence of ordered domains. The ordering process evolves from a short initial two-dimensional ordering process through a crossover region to a quasi-one-dimensional behavior. The whole process is diffusive (inverse half-width of the structure factor peak 1/q_{¦¦ t}), in contrast to a model proposed by Kawasakiet al., where an intermediate logarithmic growth law is expected. All results are completely describable in the picture of an annihilating random walk (ARW) of domain walls.     

Bond percolation for homogeneous two-dimensional lattices

Bond percolation is studied for the three homogeneous two-dimensional lattices: square lattice (SL), triangular lattice (TL) and honeycomb lattice (HL). An expanding cell technique is used to obtain percolation thresholds and other relevant information for different cell sizes. We extend the analysis as to include slightly asymmetric cells in addition to the usual symmetric cells to get more points in the scaling analysis. Exact percolation functions are obtained for each size. Then, the percolation threshold is obtained by means of two complementary methods: one based on the well-known renormalization techniques and the other one introduced here which is based upon determining the inflection point of the percolation curves. A comparison of the results obtained by these two methods is performed. The study includes iterations to extrapolate numerical results towards the thermodynamic limit. Critical exponents ν, β and γ are obtained. Values are compared with numerical results and expected theoretical estimations; present results show agreement and even improvement (in the case of γ) with respect to some numeric values available in the literature. Comparison tables are provided.     

Experimental evidence for magnetic ordering in a literally two-dimensional magnet

The electron spin resonances of literally two-dimensional magnetic structures, formed of manganese stearate by the Langmuir-Blodgett technique, have been measured down to 1.3K. In one such structure the resonance field decreased abruptly at 2.0 K by more than 1000 Oe, and was highly anisotropic below this temperature. These, and other observations can be explained by the hypothesis of weak-ferromagnetic ordering.     

Quantum criticality and percolation in dimer-diluted two-dimensional antiferromagnets

The S = 1/2 Heisenberg model is considered on bilayer and single-layer square lattices with couplings J1, J2, with each spin belonging to one J2-coupled dimer. A transition from a Néel to disordered ground state occurs at a critical value of g = J2/J1. The systems are here studied at their dimer-dilution percolation points p*. The multicritical point (g*,p*) previously found for the bilayer is not reproduced for the single layer. Instead, there is a line of critical points (g < g*, p*) with continuously varying exponents. The uniform magnetic susceptibility diverges as T(-alpha) with alpha element of [1/2,1]. This unusual behavior is attributed to an effective free-moment density approximately T(1-alpha). The susceptibility of the bilayer is not divergent but exhibits remarkably robust quantum-critical scaling.     

Entropic elasticity of two-dimensional self-avoiding percolation systems

The sol-gel transition is studied on a purely entropic two-dimensional model system consisting of hard spheres (disks) in which a fraction p of neighbors are tethered by inextensible bonds. We use a new method to measure directly the elastic properties of the system. We find that over a broad range of hard sphere diameters a the rigidity threshold is insensitive to a and indistinguishable from the percolation threshold p(c). Close to p(c), the shear modulus behaves as (p-p(c))(f), where the exponent f approximately 1. 3 is independent of a and is similar to the conductivity exponent in random resistor networks.     

The percolation perimeter for two-dimensional directed animals

The percolation perimeter to-size ratio of directed animals is investigated. For the square lattice it is found to be very close to 0.75 and the first correction is found on both the triangular and square lattices to be Bethe-like as for normal lattice animals.     

Surface roughening for two-dimensional percolation abovep c

The surfaces of large clusters above the critical concentrationp _c were Monte Carlo-simulated on a 2-dimensional square lattice. We study the widthW of the interface separating the interior of very large clusters from the outside region. The results show clearly surface roughening (at least in the simulated range). Even in the high concentration limitp→1 the interface widthW increases with the lengthL of the simulated interface, following (presumably) a square root law.