Penentration of dynamic localized states in DC-driven Josephson junction ladders by discrete jumps

We give a theoretical study of unusual resistive (dynamic) localized states in anisotropic Josephson junction ladders, driven by a DC current at one edge. These states comprise nonlinearly coupled rotating Josephson phases in adjacent cells, and with increasing current they are found to expand into neighboring cells by a sequence of sudden jumps. We argue that the jumps arise from instabilities in the ladder's superconducting part, and our analytic expressions for the peculiar voltage (rotational frequency) ratios and I-V curves are in very good agreement with direct numerical simulations.Comment: Accepted, Physical Review E. 5 pages, 5 figures. Revtex, with postscript figure

Overlap Distribution of the Three-Dimensional Ising Model

We study the Parisi overlap probability density P_L(q) for the three-dimensional Ising ferromagnet by means of Monte Carlo (MC) simulations. At the critical point P_L(q) is peaked around q=0 in contrast with the double peaked magnetic probability density. We give particular attention to the tails of the overlap distribution at the critical point, which we control over up to 500 orders of magnitude by using the multi-overlap MC algorithm. Below the critical temperature interface tension estimates from the overlap probability density are given and their approach to the infinite volume limit appears to be smoother than for estimates from the magnetization.Comment: 7 pages, RevTex, 9 Postscript figure

FINITE SIZE SCALING FOR FIRST ORDER TRANSITIONS: POTTS MODEL

The finite-size scaling algorithm based on bulk and surface renormalization of de Oliveira (1992) is tested on q-state Potts models in dimensions D = 2 and 3. Our Monte Carlo data clearly distinguish between first- and second-order phase transitions. Continuous-q analytic calculations performed for small lattices show a clear tendency of the magnetic exponent Y = D - beta/nu to reach a plateau for increasing values of q, which is consistent with the first-order transition value Y = D. Monte Carlo data confirm this trend.Comment: 5 pages, plain tex, 5 EPS figures, in file POTTS.UU (uufiles

Medium-range interactions and crossover to classical critical behavior

We study the crossover from Ising-like to classical critical behavior as a function of the range R of interactions. The power-law dependence on R of several critical amplitudes is calculated from renormalization theory. The results confirm the predictions of Mon and Binder, which were obtained from phenomenological scaling arguments. In addition, we calculate the range dependence of several corrections to scaling. We have tested the results in Monte Carlo simulations of two-dimensional systems with an extended range of interaction. An efficient Monte Carlo algorithm enabled us to carry out simulations for sufficiently large values of R, so that the theoretical predictions could actually be observed.Comment: 16 pages RevTeX, 8 PostScript figures. Uses epsf.sty. Also available as PostScript and PDF file at http://www.tn.tudelft.nl/tn/erikpubs.htm

Phase transitions in BaTiO3_3 from first principles

We develop a first-principles scheme to study ferroelectric phase transitions for perovskite compounds. We obtain an effective Hamiltonian which is fully specified by first-principles ultra-soft pseudopotential calculations. This approach is applied to BaTiO$_3$, and the resulting Hamiltonian is studied using Monte Carlo simulations. The calculated phase sequence, transition temperatures, latent heats, and spontaneous polarizations are all in good agreement with experiment. The order-disorder vs.\ displacive character of the transitions and the roles played by different interactions are discussed.Comment: 13 page

Generating a checking sequence with a minimum number of reset transitions

Given a finite state machine M, a checking sequence is an input sequence that is guaranteed to lead to a failure if the implementation under test is faulty and has no more states than M. There has been much interest in the automated generation of a short checking sequence from a finite state machine. However, such sequences can contain reset transitions whose use can adversely affect both the cost of applying the checking sequence and the effectiveness of the checking sequence. Thus, we sometimes want a checking sequence with a minimum number of reset transitions rather than a shortest checking sequence. This paper describes a new algorithm for generating a checking sequence, based on a distinguishing sequence, that minimises the number of reset transitions used.This work was supported in part by Leverhulme Trust grant number F/00275/D, Testing State Based Systems, Natural Sciences and Engineering Research Council (NSERC) of Canada grant number RGPIN 976, and Engineering and Physical Sciences Research Council grant number GR/R43150, Formal Methods and Testing (FORTEST)

Exchange anisotropy, disorder and frustration in diluted, predominantly ferromagnetic, Heisenberg spin systems

Motivated by the recent suggestion of anisotropic effective exchange interactions between Mn spins in Ga$_{1-x}$Mn$_x$As (arising as a result of spin-orbit coupling), we study their effects in diluted Heisenberg spin systems. We perform Monte Carlo simulations on several phenomenological model spin Hamiltonians, and investigate the extent to which frustration induced by anisotropic exchanges can reduce the low temperature magnetization in these models and the interplay of this effect with disorder in the exchange. In a model with low coordination number and purely ferromagnetic (FM) exchanges, we find that the low temperature magnetization is gradually reduced as exchange anisotropy is turned on. However, as the connectivity of the model is increased, the effect of small-to-moderate anisotropy is suppressed, and the magnetization regains its maximum saturation value at low temperatures unless the distribution of exchanges is very wide. To obtain significant suppression of the low temperature magnetization in a model with high connectivity, as is found for long-range interactions, we find it necessary to have both ferromagnetic and antiferromagnetic (AFM) exchanges (e.g. as in the RKKY interaction). This implies that disorder in the sign of the exchange interaction is much more effective in suppressing magnetization at low temperatures than exchange anisotropy.Comment: 9 pages, 8 figure

Phase transitions in a frustrated XY model with zig-zag couplings

We study a new generalized version of the square-lattice frustrated XY model where unequal ferromagnetic and antiferromagnetic couplings are arranged in a zig-zag pattern. The ratio between the couplings $\rho$ can be used to tune the system, continuously, from the isotropic square-lattice to the triangular-lattice frustrated XY model. The model can be physically realized as a Josephson-junction array with two different couplings, in a magnetic field corresponding to half-flux quanta per plaquette. Mean-field approximation, Ginzburg-Landau expansion and finite-size scaling of Monte Carlo simulations are used to study the phase diagram and critical behavior. Depending on the value of $\rho$, two separate transitions or a transition line in the universality class of the XY-Ising model, with combined $Z_2$ and U(1) symmetries, takes place. In particular, the phase transitions of the standard square-lattice and triangular-lattice frustrated XY models correspond to two different cuts through the same transition line. Estimates of the chiral ($Z_2$) critical exponents on this transition line deviate significantly from the pure Ising values, consistent with that along the critical line of the XY-Ising model. This suggests that a frustrated XY model or Josephson-junction array with a zig-zag coupling modulation can provide a physical realization of the XY-Ising model critical line.Comment: 11 pages, 9 figures, RevTex, to appear in Phys. Rev.

Lattice-switch Monte Carlo

We present a Monte Carlo method for the direct evaluation of the difference between the free energies of two crystal structures. The method is built on a lattice-switch transformation that maps a configuration of one structure onto a candidate configuration of the other by `switching' one set of lattice vectors for the other, while keeping the displacements with respect to the lattice sites constant. The sampling of the displacement configurations is biased, multicanonically, to favor paths leading to `gateway' arrangements for which the Monte Carlo switch to the candidate configuration will be accepted. The configurations of both structures can then be efficiently sampled in a single process, and the difference between their free energies evaluated from their measured probabilities. We explore and exploit the method in the context of extensive studies of systems of hard spheres. We show that the efficiency of the method is controlled by the extent to which the switch conserves correlated microstructure. We also show how, microscopically, the procedure works: the system finds gateway arrangements which fulfill the sampling bias intelligently. We establish, with high precision, the differences between the free energies of the two close packed structures (fcc and hcp) in both the constant density and the constant pressure ensembles.Comment: 34 pages, 9 figures, RevTeX. To appear in Phys. Rev.

Monte Carlo simulations of an impurity band model for III-V diluted magnetic semiconductors

We report the results of a Monte Carlo study of a model of (III,Mn)V diluted magnetic semiconductors which uses an impurity band description of carriers coupled to localized Mn spins and is applicable for carrier densities below and around the metal-insulator transition. In agreement with mean field studies, we find a transition to a ferromagnetic phase at low temperatures. We compare our results for the magnetic properties with the mean field approximation, as well as with experiments, and find favorable qualitative agreement with the latter. The local Mn magnetization below the Curie temperature is found to be spatially inhomogeneous, and strongly correlated with the local carrier charge density at the Mn sites. The model contains fermions and classical spins and hence we introduce a perturbative Monte Carlo scheme to increase the speed of our simulations.Comment: 17 pages, 24 figures, 2 table