arXiv subjects

J. M. Kosterlitz

Publications and source records attributed to J. M. Kosterlitz.

At least 19 recordsLinked to original sources

arXiv2022

Topology, Vorticity and Limit Cycle in a Stabilized Kuramoto-Sivashinsky Equation

A noisy stabilized Kuramoto-Sivashinsky equation is analyzed by stochastic decomposition. For values of control parameter for which periodic stationary patterns exist, the dynamics can be decomposed into diffusive and transverse parts which act on a stochastic potential. The relative positions of stationary states in the stochastic global potential landscape can be obtained from the topology spanned by the low-lying eigenmodes which inter-connect them. Numerical simulations confirm the predicted landscape. The transverse component also predicts a universal class of vortex like circulations around fixed points. These drive nonlinear drifting and limit cycle motion of the underlying periodic structure in certain regions of parameter space. Our findings might be relevant in studies of other nonlinear systems such as deep learning neural networks.

nlin.AO↗

arXiv2019

Wavenumber Selection in Pattern Forming Systems

Wavenumber selection in pattern forming systems remains a long standing puzzle in physics. Previous studies have shown that external noise is a possible mechanism for wavenumber selection. We conduct an extensive numerical study of the noisy stabilized Kuramoto Sivashinsky equation. We use a fast spectral method of integration, which enables us to investigate long time behavior for large system sizes that could not be investigated by earlier work. We find that a state with a unique wavenumber has the highest probability of occurring at very long times. We also find that this state is independent of the strength of the noise and initial conditions, thus making a convincing case for the role of noise as a mechanism of state selection.

nlin.PS↗

arXiv2015

Consistent Hydrodynamics for Phase Field Crystals

We use the amplitude expansion in the phase field crystal framework to formulate an approach where the fields describing the microscopic structure of the material are coupled to a hydrodynamic velocity field. The model is shown to reduce to the well known macroscopic theories in appropriate limits, including compressible Navier-Stokes and wave equations. Moreover, we show that the dynamics proposed allows for long wavelength phonon modes and demonstrate the theory numerically showing that the elastic excitations in the system are relaxed through phonon emission.

cond-mat.stat-mech↗

arXiv2010

State selection in the noisy stabilized Kuramoto-Sivashinsky equation

In this work, we study the 1D stabilized Kuramoto Sivashinsky equation with additive uncorrelated stochastic noise. The Eckhaus stable band of the deterministic equation collapses to a narrow region near the center of the band. This is consistent with the behavior of the phase diffusion constants of these states. Some connections to the phenomenon of state selection in driven out of equilibrium systems are made.

cond-mat.stat-mech↗

arXiv2005

Pattern Selection in a Phase Field Model for Directional Solidification

A symmetric phase field model is used to study wavelength selection in two dimensions. We study the problem in a finite system using a two-pronged approach. First we construct an action and, minimizing this, we obtain the most probable configuration of the system, which we identify with the selected stationary state. The minimization is constrained by the stationary solutions of stochastic evolution equations and is done numerically. Secondly, additional support for this selected state is obtained from straightforward simulations of the dynamics from a variety of initial states.

cond-mat.stat-mech↗

arXiv2002

Screened Vortex Lattice Model with Disorder

The three dimensional XY model with quenched random disorder and finite screening is studied. We argue that the system scales to model with $λ\simeq 0\simeq T$ and the resulting effective model is studied numerically by defect energy scaling. In zero external field we find that there exists a true superconducting phase with a stiffness exponent $θ\simeq +1.0$ for weak disorder. For low magnetic field and weak disorder, there is also a superconducting phase with $θ\simeq +1.0$ which we conjecture is a Bragg glass. For larger disorder or applied field, there is a non superconducting phase with $θ\simeq -1.0$. We estimate the critical external field whose value is consistent with experiment.

cond-mat.stat-mech↗

arXiv2002

Domain Wall Renormalization Group Study of XY Model with Quenched Random Phase Shifts

The XY model with quenched random disorder is studied by a zero temperature domain wall renormalization group method in 2D and 3D. Instead of the usual phase representation we use the charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations yield spin stiffness exponents $θ_{s} \approx -0.36$ in 2D and $θ_{s} \approx +0.31$ in 3D, which are considerably larger than previous estimates and strongly suggest that the lower critical dimension is less than three. For the $\pm J$ XY spin glass in 3D, we obtain a spin stiffness exponent $θ_{s} \approx +0.10$ which supports the existence of spin glass order at finite temperature in contrast with previous estimates which obtain $θ_{s}< 0$. Our method also allows us to study renormalization group flows of both the coupling constant and the disorder strength with length scale $L$. Our results are consistent with recent analytic and numerical studies suggesting the absence of a re-entrant transition in 2D at low temperature. Some possible consequences and connections with real vortex systems are discussed.

cond-mat.stat-mech↗

arXiv2000

Sharp interface limits of phase-field models

The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and the solidification of eutectic alloys. The projection operator method is used to extract the ``sharp interface limit'' from phase field models which have interfaces that are diffuse on a length scale $ξ$. In particular,phase-field equations are mapped onto sharp interface equations in the limits $ξκ\ll 1$ and $ξv/D \ll 1$, where $κ$ and $v$ are respectively the interface curvature and velocity and $D$ is the diffusion constant in the bulk. The calculations provide one general set of sharp interface equations that incorporate the Gibbs-Thomson condition, the Allen-Cahn equation and the Kardar-Parisi-Zhang equation.

cond-mat.soft↗

arXiv1998

Charge glass in two-dimensional arrays of capacitively coupled grains with random offset charges

We study the effect of random offset charges in the insulator to conductor transition in systems of capacitively coupled grains, as realized in two-dimensional arrays of ultrasmall Josephson junctions. In presence of disorder, the conductive transition and charge ordering at nonzero gate voltages are both destroyed for any degree of disorder $σ$ at finite temperatures $T$, in the thermodynamic limit, but crossover effects will dominate at length scales smaller than $ξ_{σ, T}=T^{-ν} f(σT^{-ν})$, where $ν$ is the thermal critical exponent of the zero-temperature charge glass transition. The conductance is linear and thermally activated but nonlinear behavior sets in at a crossover voltage which decreases as temperature decreases. For large disorder, the results are supported by Monte Carlo dynamics simulations of a Coulomb gas with offset charges and are consistent with the thermally activated behavior found in recent experiments.

cond-mat.dis-nn↗

arXiv1998

Numerical Study of Order in a Gauge Glass Model

The XY model with quenched random phase shifts is studied by a T=0 finite size defect energy scaling method in 2d and 3d. The defect energy is defined by a change in the boundary conditions from those compatible with the true ground state configuration for a given realization of disorder. A numerical technique, which is exact in principle, is used to evaluate this energy and to estimate the stiffness exponent $θ$. This method gives $θ= -0.36\pm0.013$ in 2d and $θ= +0.31\pm 0.015$ in 3d, which are considerably larger than previous estimates, strongly suggesting that the lower critical dimension is less than three. Some arguments in favor of these new estimates are given.

cond-mat.stat-mech↗

arXiv1998

Numerical Study of Spin and Chiral Order in a Two-Dimensional XY Spin Glass

The two dimensional XY spin glass is studied numerically by a finite size scaling method at T=0 in the vortex representation which allows us to compute the exact (in principle) spin and chiral domain wall energies. We confirm earlier predictions that there is no glass phase at any finite T. Our results strongly support the conjecture that both spin and chiral order have the same correlation length exponent $ν\approx 2.70$. We obtain preliminary results in 3d.

cond-mat.stat-mech↗

arXiv1998

A Simple Model for Anisotropic Step Growth

We consider a simple model for the growth of isolated steps on a vicinal crystal surface. It incorporates diffusion and drift of adatoms on the terrace, and strong step and kink edge barriers. Using a combination of analytic methods and Monte Carlo simulations, we study the morphology of growing steps in detail. In particular, under typical Molecular Beam Epitaxy conditions the step morphology is linearly unstable in the model and develops fingers separated by deep cracks. The vertical roughness of the step grows linearly in time, while horizontally the fingers coarsen proportional to $t^{0.33}$. We develop scaling arguments to study the saturation of the ledge morphology for a finite width and length of the terrace.

cond-mat.mtrl-sci↗

arXiv1997

Edge effects in a frustrated Josephson junction array with modulated couplings

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 $R_{L}(T)\sim A(T)/L$ with $ A(T) \propto (T-T_{cI})$ at intermediate temperatures $T_{cXY}>T>T_{cI}$ 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.

cond-mat.supr-con↗

arXiv1997

Numerical Study of a Superconducting Glass Model

An XY model with random phase shifts as a model for a superconducting glass is studied in two and three dimensions by a zero temperature domain wall renormalization group which allows one to follow the flows of both the coupling constant and the disorder strength with increasing length scale. Weak disorder is found to be marginal in two and probably irrelevant in three dimensions. For strong disorder the flow is towards a non-superconducting gauge glass fixed point in 2d and a superconducting glass in 3d. Our results are in agreement with recent analytic theory and are inconsistent with earlier predictions of a re-entrant transition to a disordered phase at very low temperature and with the loss of superconductivity for any finite amount of disorder.

cond-mat.supr-con↗

arXiv1997

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

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, $T>T_{KT}$, 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.

cond-mat.supr-con↗

arXiv1996

Phase diagram of the restricted solid-on-solid model coupled to the Ising model

We study the phase transitions of a restricted solid-on-solid model coupled to an Ising model, which can be derived from the coupled XY-Ising model. There are two kinds of phase transition lines. One is a Ising transition line and the other is surface roughening transition line. The latter is a KT transition line from the viewpoint of the XY model. Using a microcanonical Monte Carlo technique, we obtain a very accurate two dimensional phase diagram. The two transition lines are separate in all the parameter space we study. This result is strong evidence that the fully frustrated XY model orders by two separate transitions and that roughening and reconstruction transitions of crystal surfaces occur separately.

cond-mat.stat-mech↗

arXiv1995

Critical behavior of Josephson-junction arrays at f=1/2

The critical behavior of frustrated Josephson-junction arrays at $f=1/2$ flux quantum per plaquette is considered. Results from Monte Carlo simulations and transfer matrix computations support the identification of the critical behavior of the square and triangular classical arrays and the one-dimensional quantum ladder with the universality class of the XY-Ising model. In the quantum ladder, the transition can happen either as a simultaneous ordering of the $Z_2$ and $U(1)$ order parameters or in two separate stages, depending on the ratio between interchain and intrachain Josephson couplings. For the classical arrays, weak random plaquette disorder acts like a random field and positional disorder as random bonds on the $Z_2$ variables. Increasing positional disorder decouples the $Z_2$ and $U(1)$ variables leading to the same critical behavior as for integer $f$.

cond-mat↗

arXiv1995

Conformal Anomaly and Critical Exponents of the XY-Ising Model

We use extensive Monte Carlo transfer matrix calculations on infinite strips of widths $L$ up to 30 lattice spacing and a finite-size scaling analysis to obtain critical exponents and conformal anomaly number $c$ for the two-dimensional $XY$-Ising model. This model is expected to describe the critical behavior of a class of systems with simultaneous $U(1)$ and $Z_2$ symmetries of which the fully frustrated $XY$ model is a special case. The effective values obtained for $c$ show a significant decrease with $L$ at different points along the line where the transition to the ordered phase takes place in a single transition. Extrapolations based on power-law corrections give values consistent with $c=3/2$ although larger values can not be ruled out. Critical exponents are obtained more accurately and are consistent with previous Monte Carlo simulations suggesting new critical behavior and with recent calculations for the frustrated $XY$ model.

cond-mat↗