34 research outputs found

    Equilibrium crystal shapes in the Potts model

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    The three-dimensional qq-state Potts model, forced into coexistence by fixing the density of one state, is studied for q=2q=2, 3, 4, and 6. As a function of temperature and number of states, we studied the resulting equilibrium droplet shapes. A theoretical discussion is given of the interface properties at large values of qq. We found a roughening transition for each of the numbers of states we studied, at temperatures that decrease with increasing qq, but increase when measured as a fraction of the melting temperature. We also found equilibrium shapes closely approaching a sphere near the melting point, even though the three-dimensional Potts model with three or more states does not have a phase transition with a diverging length scale at the melting point.Comment: 6 pages, 3 figures, submitted to PR

    Properties of Interfaces in the two and three dimensional Ising Model

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    To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the 2D2D and 3D3D Ising model. Following Binder we extract the interfacial free energy from the infinite volume limit of the magnetic probability density. Stringent tests of the numerical methods are performed by reproducing with high precision exact 2D2D results. In the physically more interesting 3D3D case we estimate the amplitude F0sF^s_0 of the critical interfacial tension Fs=F0stΌF^s = F^s_0 t^\mu to be F0s=1.52±0.05F^s_0 = 1.52 \pm 0.05. This result is in good agreement with a previous MC calculation by Mon, as well as with experimental results for related amplitude ratios. In addition, we study in some details the shape of the magnetic probability density for temperatures below the Curie point.Comment: 25 pages; sorry no figures include

    Monte Carlo Renormalization Group Analysis of Lattice ϕ4\phi^4 Model in D=3,4D=3,4

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    We present a simple, sophisticated method to capture renormalization group flow in Monte Carlo simulation, which provides important information of critical phenomena. We applied the method to D=3,4D=3,4 lattice ϕ4\phi^4 model and obtained renormalization flow diagram which well reproduces theoretically predicted behavior of continuum ϕ4\phi^4 model. We also show that the method can be easily applied to much more complicated models, such as frustrated spin models.Comment: 13 pages, revtex, 7 figures. v1:Submitted to PRE. v2:considerably reduced redundancy of presentation. v3:final version to appear in Phys.Rev.

    Finite Size and Current Effects on IV Characteristics of Josephson Junction Arrays

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    The effects of finite size and of finite current on the current-voltage characteristics of Josephson junction arrays is studied both theoretically and by numerical simulations. The cross-over from non-linear to linear behavior at low temperature is shown to be a finite size effect and the non-linear behavior at higher temperature, T>TKTT>T_{KT}, is shown to be a finite current effect. These are argued to result from competition between the three length scales characterizing the system. The importance of boundary effects is discussed and it is shown that these may dominate the behavior in small arrays.Comment: 5 pages, figures included, to appear in PR

    Medium-range interactions and crossover to classical critical behavior

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    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

    Transfer-Matrix Monte Carlo Estimates of Critical Points in the Simple Cubic Ising, Planar and Heisenberg Models

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    The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the statistical noise can be reduced considerably by a similarity transformation of the transfer matrix using a variational estimate of its leading eigenvector, in analogy with a common practice in various quantum Monte Carlo techniques. Here we take the two-dimensional coupled XYXY-Ising model as an example. Furthermore, we calculate interface free energies of finite three-dimensional O(nn) models, for the three cases n=1n=1, 2 and 3. Application of finite-size scaling to the numerical results yields estimates of the critical points of these three models. The statistical precision of the estimates is satisfactory for the modest amount of computer time spent

    Structure of wavefunctions in (1+2)-body random matrix ensembles

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    Abstrtact: Random matrix ensembles defined by a mean-field one-body plus a chaos generating random two-body interaction (called embedded ensembles of (1+2)-body interactions) predict for wavefunctions, in the chaotic domain, an essentially one parameter Gaussian forms for the energy dependence of the number of principal components NPC and the localization length {\boldmath l}_H (defined by information entropy), which are two important measures of chaos in finite interacting many particle systems. Numerical embedded ensemble calculations and nuclear shell model results, for NPC and {\boldmath l}_H, are compared with the theory. These analysis clearly point out that for realistic finite interacting many particle systems, in the chaotic domain, wavefunction structure is given by (1+2)-body embedded random matrix ensembles.Comment: 20 pages, 3 figures (1a-c, 2a-b, 3a-c), prepared for the invited talk given in the international conference on `Perspectives in Theoretical Physics', held at Physical Research Laboratory, Ahmedabad during January 8-12, 200

    Domain Walls Motion and Resistivity in a Fully-Frustrated Josephson Array

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    It is identified numerically that the resistivity of a fully-frustrated Josephson-junction array is due to motion of domain walls in vortex lattice rather than to motion of single vortices

    Edge effects in a frustrated Josephson junction array with modulated couplings

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    A square array of Josephson junctions with modulated strength in a magnetic field with half a flux quantum per plaquette is studied by analytic arguments and dynamical simulations. The modulation is such that alternate columns of junctions are of different strength to the rest. Previous work has shown that this system undergoes an XY followed by an Ising-like vortex lattice disordering transition at a lower temperature. We argue that resistance measurements are a possible probe of the vortex lattice disordering transition as the linear resistance RL(T)∌A(T)/LR_{L}(T)\sim A(T)/L with A(T)∝(T−TcI) A(T) \propto (T-T_{cI}) at intermediate temperatures TcXY>T>TcIT_{cXY}>T>T_{cI} due to dissipation at the array edges for a particular geometry and vanishes for other geometries. Extensive dynamical simulations are performed which support the qualitative physical arguments.Comment: 8 pages with figs, RevTeX, to appear in Phys. Rev.

    Vortex dynamics for two-dimensional XY models

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    Two-dimensional XY models with resistively shunted junction (RSJ) dynamics and time dependent Ginzburg-Landau (TDGL) dynamics are simulated and it is verified that the vortex response is well described by the Minnhagen phenomenology for both types of dynamics. Evidence is presented supporting that the dynamical critical exponent zz in the low-temperature phase is given by the scaling prediction (expressed in terms of the Coulomb gas temperature TCGT^{CG} and the vortex renormalization given by the dielectric constant Ï”~\tilde\epsilon) z=1/Ï”~TCG−2≄2z=1/\tilde{\epsilon}T^{CG}-2\geq 2 both for RSJ and TDGL and that the nonlinear IV exponent a is given by a=z+1 in the low-temperature phase. The results are discussed and compared with the results of other recent papers and the importance of the boundary conditions is emphasized.Comment: 21 pages including 15 figures, final versio
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