Finite-Size Scaling Critical Behavior of Randomly Pinned Spin-Density Waves

We have performed Monte Carlo studies of the 3D $XY$ model with random uniaxial anisotropy, which is a model for randomly pinned spin-density waves. We study $L \times L \times L$ simple cubic lattices, using $L$ values in the range 16 to 64, and with random anisotropy strengths of $D / 2 J$ = 1, 2, 3, 6 and $\infty$. There is a well-defined finite temperature critical point, $T_c$, for each these values of $D / 2 J$. We present results for the angle-averaged magnetic structure factor, $S (k)$ at $T_c$ for $L = 64$. We also use finite-size scaling analysis to study scaling functions for the critical behavior of the specific heat, the magnetization and the longitudinal magnetic susceptibility. Good data collapse of the scaling functions over a wide range of $T$ is seen for $D / 2 J$ = 6 and $\infty$. For our finite values of $D / 2 J$ the scaled magnetization function increases with $L$ below $T_c$, and appears to approach an $L$-independent limit for large $L$. This suggests that the system is ferromagnetic below $T_c$.Comment: 21 pages in single column format, 20 .eps files, revised and expanded, errors corrected, submitted to PR

Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D ±J\pm J Random-Bond Ising Model

The statistics of the ground-state and domain-wall energies for the two-dimensional random-bond Ising model on square lattices with independent, identically distributed bonds of probability $p$ of $J_{ij}= -1$ and $(1-p)$ of $J_{ij}= +1$ are studied. We are able to consider large samples of up to $320^2$ spins by using sophisticated matching algorithms. We study $L \times L$ systems, but we also consider $L \times M$ samples, for different aspect ratios $R = L / M$. We find that the scaling behavior of the ground-state energy and its sample-to-sample fluctuations inside the spin-glass region ($p_c \le p \le 1 - p_c$) are characterized by simple scaling functions. In particular, the fluctuations exhibit a cusp-like singularity at $p_c$. Inside the spin-glass region the average domain-wall energy converges to a finite nonzero value as the sample size becomes infinite, holding $R$ fixed. Here, large finite-size effects are visible, which can be explained for all $p$ by a single exponent $\omega\approx 2/3$, provided higher-order corrections to scaling are included. Finally, we confirm the validity of aspect-ratio scaling for $R \to 0$: the distribution of the domain-wall energies converges to a Gaussian for $R \to 0$, although the domain walls of neighboring subsystems of size $L \times L$ are not independent.Comment: 11 pages with 15 figures, extensively revise

General solution of classical master equation for reducible gauge theories

We give the general solution to the classical master equation (S,S)=0 for reducible gauge theories. To this aim, we construct a new coordinate system in the extended configuration space and transform the equation by changing variables. Then it can be solved by an iterative method.Comment: 15 pages; v3: refs. added, section 4 substantially improved, a section added; v4: reference and example adde

Regularisation, the BV method, and the antibracket cohomology

We review the Lagrangian Batalin--Vilkovisky method for gauge theories. This includes gauge fixing, quantisation and regularisation. We emphasize the role of cohomology of the antibracket operation. Our main example is $d=2$ gravity, for which we also discuss the solutions for the cohomology in the space of local integrals. This leads to the most general form for the action, for anomalies and for background charges.Comment: 12 pages, LaTeX, Preprint-KUL-TF-94/2

Random Field and Random Anisotropy Effects in Defect-Free Three-Dimensional XY Models

Monte Carlo simulations have been used to study a vortex-free XY ferromagnet with a random field or a random anisotropy on simple cubic lattices. In the random field case, which can be related to a charge-density wave pinned by random point defects, it is found that long-range order is destroyed even for weak randomness. In the random anisotropy case, which can be related to a randomly pinned spin-density wave, the long-range order is not destroyed and the correlation length is finite. In both cases there are many local minima of the free energy separated by high entropy barriers. Our results for the random field case are consistent with the existence of a Bragg glass phase of the type discussed by Emig, Bogner and Nattermann.Comment: 10 pages, including 2 figures, extensively revise

Effect of Anode Dielectric Coating on Hall Thruster Operation

An interesting phenomenon observed in the near-anode region of a Hall thruster is that the anode fall changes from positive to negative upon removal of the dielectric coating, which is produced on the anode surface during the normal course of Hall thruster operation. The anode fall might affect the thruster lifetime and acceleration efficiency. The effect of the anode coating on the anode fall is studied experimentally using both biased and emissive probes. Measurements of discharge current oscillations indicate that thruster operation is more stable with the coated anode

Power-law correlations and orientational glass in random-field Heisenberg models

Monte Carlo simulations have been used to study a discretized Heisenberg ferromagnet (FM) in a random field on simple cubic lattices. The spin variable on each site is chosen from the twelve [110] directions. The random field has infinite strength and a random direction on a fraction x of the sites of the lattice, and is zero on the remaining sites. For x = 0 there are two phase transitions. At low temperatures there is a [110] FM phase, and at intermediate temperature there is a [111] FM phase. For x > 0 there is an intermediate phase between the paramagnet and the ferromagnet, which is characterized by a |k|^(-3) decay of two-spin correlations, but no true FM order. The [111] FM phase becomes unstable at a small value of x. At x = 1/8 the [110] FM phase has disappeared, but the power-law correlated phase survives.Comment: 8 pages, 12 Postscript figure

Generalized Classical BRST Cohomology and Reduction of Poisson Manifolds

In this paper, we formulate a generalization of the classical BRST construction which applies to the case of the reduction of a poisson manifold by a submanifold. In the case of symplectic reduction, our procedure generalizes the usual classical BRST construction which only applies to symplectic reduction of a symplectic manifold by a coisotropic submanifold, \ie\ the case of reducible ``first class'' constraints. In particular, our procedure yields a method to deal with ``second-class'' constraints. We construct the BRST complex and compute its cohomology. BRST cohomology vanishes for negative dimension and is isomorphic as a poisson algebra to the algebra of smooth functions on the reduced poisson manifold in zero dimension. We then show that in the general case of reduction of poisson manifolds, BRST cohomology cannot be identified with the cohomology of vertical differential forms.Comment: 3

Bi-defects of Nematic Surfactant Bilayers

We consider the effects of the coupling between the orientational order of the two monolayers in flat nematic bilayers. We show that the presence of a topological defect on one bilayer generates a nontrivial orientational texture on both monolayers. Therefore, one cannot consider isolated defects on one monolayer, but rather associated pairs of defects on either monolayer, which we call bi-defects. Bi-defects generally produce walls, such that the textures of the two monolayers are identical outside the walls, and different in their interior. We suggest some experimental conditions in which these structures could be observed.Comment: RevTeX, 4 pages, 3 figure

Power-law correlated phase in random-field XY models and randomly pinned charge-density waves

Monte Carlo simulations have been used to study the Z6 ferromagnet in a random field on simple cubic lattices, which is a simple model for randomly pinned charge-density waves. The random field is chosen to have infinite strength on a fraction x of the sites of the lattice, and to be zero on the remaining sites. For x= 1/16 there are two phase transitions. At low temperature there is a ferromagnetic phase, which is stabilized by the six-fold nonrandom anisotropy. The intermediate temperature phase is characterized by a |k|^(-3) decay of two-spin correlations, but no true ferromagnetic order. At the transition between the power-law correlated phase and the paramagnetic phase the magnetic susceptibility diverges, and the two-spin correlations decay approximately as |k|^(-2.87).Comment: 16 pages, 8 figures, Postscrip