arXiv subjects

M. A. Moore

Publications and source records attributed to M. A. Moore.

At least 91 records · Page 5Linked to original sources

arXiv2000

Stretched exponential relaxation in the mode-coupling theory for the Kardar-Parisi-Zhang equation

We study the mode-coupling theory for the Kardar-Parisi-Zhang equation in the strong-coupling regime, focusing on the long time properties. By a saddle point analysis of the mode-coupling equations, we derive exact results for the correlation function in the long time limit - a limit which is hard to study using simulations. The correlation function at wavevector k in dimension d is found to behave asymptotically at time t as C(k,t)\simeq 1/k^{d+4-2z} (Btk^z)^{γ/z} e^{-(Btk^z)^{1/z}}, with γ=(d-1)/2, A a determined constant and B a scale factor.

cond-mat.stat-mech↗

arXiv2000

Upper critical dimension, dynamic exponent and scaling functions in the mode-coupling theory for the Kardar-Parisi-Zhang equation

We study the mode-coupling approximation for the KPZ equation in the strong coupling regime. By constructing an ansatz consistent with the asymptotic forms of the correlation and response functions we determine the upper critical dimension d_c=4, and the expansion z=2-(d-4)/4+O((4-d)^2) around d_c. We find the exact z=3/2 value in d=1, and estimate the values 1.62, 1.78 for z, in d=2,3. The result d_c=4 and the expansion around d_c are very robust and can be derived just from a mild assumption on the relative scale on which the response and correlation functions vary as z approaches 2.

cond-mat.stat-mech↗

arXiv2000

Spin glasses without time-reversal symmetry and the absence of a genuine structural glass transition

We study the three-spin model and the Ising spin glass in a field using Migdal-Kadanoff approximation. The flows of the couplings and fields indicate no phase transition, but they show even for the three-spin model a slow crossover to the asymptotic high-temperature behaviour for strong values of the couplings. We also evaluated a quantity that is a measure of the degree of non-self-averaging, and we found that it can become large for certain ranges of the parameters and the system sizes. For the spin glass in a field the maximum of non-self-averaging follows for given system size a line that resembles the de Almeida-Thouless line. We conclude that non-self-averaging found in Monte-Carlo simulations cannot be taken as evidence for the existence of a low-temperature phase with replica-symmetry breaking. Models similar to the three-spin model have been extensively discussed in order to provide a description of structural glasses. Their theory at mean-field level resembles the mode-coupling theory of real glasses. At that level the one-step replica symmetry approach breaking predicts two transitions, the first transition being dynamical and the second thermodynamical. Our results suggest that in real finite dimensional glasses there will be no genuine transitions at all, but that some features of mean-field theory could still provide some useful insights.

cond-mat.dis-nn↗

arXiv1999

The Link Overlap and Finite Size Effects for the 3D Ising Spin Glass

We study the link overlap between two replicas of an Ising spin glass in three dimensions using the Migdal-Kadanoff approximation and scaling arguments based on the droplet picture. For moderate system sizes, the distribution of the link overlap shows the asymmetric shape and large sample-to-sample variations found in Monte Carlo simulations and usually attributed to replica symmetry breaking. However, the scaling of the width of the distribution, and the link overlap in the presence of a weak coupling between the two replicas are in agreement with the droplet picture. We also discuss why it is impossible to see the asymptotic droplet-like behaviour for moderate system sizes and temperatures not too far below the critical temperature.

cond-mat.dis-nn↗

arXiv1999

Symmetric patterns of dislocations in Thomson's problem

Determination of the classical ground state arrangement of $N$ charges on the surface of a sphere (Thomson's problem) is a challenging numerical task. For special values of $N$ we have obtained using the ring removal method of Toomre, low energy states in Thomson's problem which have icosahedral symmetry where lines of dislocations run between the 12 disclinations which are induced by the spherical geometry into the near triangular lattice which forms on a local scale.

cond-mat↗

arXiv1999

Reply to "Comment on Evidence for the droplet picture of spin glasses"

Using Monte Carlo simulations (MCS) and the Migdal-Kadanoff approximation (MKA), Marinari et al. study in their comment on our paper the link overlap between two replicas of a three-dimensional Ising spin glass in the presence of a coupling between the replicas. They claim that the results of the MCS indicate replica symmetry breaking (RSB), while those of the MKA are trivial, and that moderate size lattices display the true low temperature behavior. Here we show that these claims are incorrect, and that the results of MCS and MKA both can be explained within the droplet picture.

cond-mat.dis-nn↗

arXiv1998

Absence of a Finite-Temperature Melting Transition in the Classical Two-Dimensional One-Component Plasma

Vortices in thin-film superconductors are often modelled as a system of particles interacting via a repulsive logarithmic potential. Arguments are presented to show that the hypothetical (Abrikosov) crystalline state for such particles is unstable at any finite temperature against proliferation of screened disclinations. The correlation length of crystalline order is predicted to grow as $\sqrt{1/T}$ as the temperature $T$ is reduced to zero, in excellent agreement with our simulations of this two-dimensional system.

cond-mat.supr-con↗

arXiv1998

Comment on "General Method to Determine Replica Symmetry Breaking Transitions"

In a recent letter Marinari et al [Phys. Rev. Lett. 81, 1698 (1998)] introduced a new method to study spin glass transitions and argued that by probing replica symmetry (RS) as opposed to time reversal symmetry (TRS), their method unambiguously shows that replica symmetry breaking (RSB) occurs in short-range spin glasses. In this comment we show that while the new method is indeed useful for studying transitions in systems where TRS is absent (such as the p-spin model studied by them), the conclusion that it shows the existence of RSB in short-range spin glasses is wrong.

cond-mat.dis-nn↗

arXiv1998

Numerical studies of the phase diagram of layered type II superconductors in a magnetic field

We report on simulations of layered superconductors using the Lawrence-Doniach model in the framework of the lowest Landau level approximation. We find a first order phase transition with a $B(T)$ dependence which agrees very well with the experimental ``melting'' line in YBaCuO. The transition is not associated with vortex lattice melting, but separates two vortex liquid states characterised by different degrees of short-range crystalline order and different length scales of correlations between vortices in different layers. The transition line ends at a critical end-point at low fields. We find the magnetization discontinuity and the location of the lower critical magnetic field to be in good agreement with experiments in YBaCuO. Length scales of order parameter correlations parallel and perpendicular to the magnetic field increase exponentially as 1/T at low temperatures. The dominant relaxation time scales grow roughly exponentially with these correlation lengths. We find that the first order phase transition persists in the presence of weak random point disorder but can be suppressed entirely by strong disorder. No vortex glass or Bragg glass state is found in the presence of disorder. The consistency of our numerical results with various experimental features in YBaCuO, including the dependence on anisotropy, and the temperature dependence of the structure factor at the Bragg peaks in neutron scattering experiments is demonstrated.

cond-mat.supr-con↗

arXiv1998

Evidence for the droplet/scaling picture of spin glasses

We have studied the Parisi overlap distribution for the three dimensional Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the full Parisi replica symmetry breaking, just as was also observed in recent Monte Carlo simulations on a cubic lattice. However, for lower temperatures our data agree with predictions from the droplet or scaling picture. The failure to see droplet model behaviour in Monte Carlo simulations is due to the fact that all existing simulations have been done at temperatures too close to the transition temperature so that sytem sizes larger than the correlation length have not been achieved.

cond-mat.dis-nn↗

arXiv1998

The Low-Field Critical End Point of the First Order Transition Line in YBCO

We report on simulations of the first order phase transition in YBCO using the Lawrence-Doniach model. We find that the magnetization discontinuity vanishes and the first order transition line ends at a critical end point for low magnetic fields in agreement with experiment. The transition is not associated with vortex lattice melting, but separates two vortex liquid states characterized by different degrees of short-range crystalline order and different length scales of correlations between vortices in different layers.

cond-mat.supr-con↗

arXiv1998

Simulations of Two-Dimensional Melting on the Surface of a Sphere

We have simulated a system of classical particles confined on the surface of a sphere interacting with a repulsive $r^{-12}$ potential. The same system simulated on a plane with periodic boundary conditions has van der Waals loops in pressure-density plots which are usually interpreted as evidence for a first order melting transition, but on the sphere such loops are absent. We also investigated the structure factor and from the width of the first peak as a function of density we can show that the growth of the correlation length is consistent with KTHNY theory. This suggests that simulations of two dimensional melting phenomena are best performed on the surface of a sphere.

cond-mat.stat-mech↗

arXiv1997

A study of nonlocal conductivity in high-temperature superconductors

We examine nonlocal conductivity in high-temperature superconductors from a phenomenological point of view. One wants to deduce the properties of the conductivity, especially its inherent length scales, from the transport data. Although this is a challenging inverse problem, complicated further by the experimental data not being completely self-consistent, we have made some progress. We find that if a certain form for the conductivity is postulated then one requires positive "viscosity" coefficients to reproduce some of the experimental results. We are able to show that the effects of surfaces on the conductivity are likely to be important and draw comparisons with the treatment of the surface within the hydrodynamic approach put forth by Huse and Majumdar. We also develop an approximation scheme for the conductivity which is more robust than the hydrodynamic one, since it is stable for both positive and negative viscosity coefficients, and discuss the results obtained using it.

cond-mat.supr-con↗

arXiv1997

Non-integer flux quanta for a spherical superconductor

A thin film superconductor shaped into a spherical shell at whose center lies the end of long thin solenoid in which there is an integer flux $NΦ_0$ has been previously extensively studied numerically as a model of a two-dimensional superconductor. The emergent flux from the solenoid produces a radial B-field at the superconducting shell and $N$ vortices in the superconducting film. We study here the effects of including a second solenoid (carrying a flux $f$) which is inserted inside the first solenoid but passing right across the sphere. This Aharonov-Bohm (AB) flux does not have to be quantized to make the order parameter single valued. The Ginzburg-Landau (GL) free energy is minimized at fixed $N$ as a function of $f$ and it is found that the minimum is usually achieved when the AB flux $f$ is half a flux quantum, but depending on $N$ the minimum may be at $f=0$ or values which are not obvious rational fractions.

cond-mat.supr-con↗

arXiv1997

Finite size effects as the explanation of ``freezing'' in vortex liquids

We investigate the effect of thermal fluctuations on the (mean-field) Abrikosov phase. The lower critical dimension of the superconducting phase is three, indicating the absence of the Abrikosov phase for dimensions d<3. Within the d=3 vortex liquid, the phase correlation length along the magnetic field direction grows exponentially rapidly as the temperature is lowered. For a finite bulk system, there is a 3D-2D crossover effect when the phase correlation length becomes comparable to the sample thickness. Such a crossover effect takes place over a very narrow temperature interval and mimics the ``first order transition'' seen in experiments on clean YBCO and BSCCO crystals. We calculate the jumps in the entropy, magnetization and specific heat due to the crossover and find reasonably good agreement with experiments on both YBCO and BSCCO.

cond-mat.supr-con↗

arXiv1997

Flux Line Lattices in Artificially Layered Superconductors

The flux line lattice of superconductors has been investigated when there exists a periodicity in the underlying system, such as can occur in artificially layered structures. For small fields parallel to the layers the flux lines enter the sample in sequential rows, with the possibility of jumps in the magnetization as new rows are created. As the field is increased these discontinuities gradually decrease, but there still exist transitions between states that are aligned differently to the periodic direction. Increasing the magnitude of the periodic potential reduces the competition between differently aligned lattices and tends to lock in one particular alignment. The effect of transitions on the shear modulus is also discussed and related to the experiments of Theunissen et al.

cond-mat↗

arXiv1997

Mixed phases in U(N) superconductivity

We consider a general class of type-II superconductors which are described by N complex order parameters (OP), with an overall U(N) symmetry for the energy functional. In the lowest energy state, each OP adopts its own particular lattice structure, making the spatial variation of the overall condensate very complex. We present detailed results for the case N=2. We also treat the limit N -> infinity, which allows us to resolve a recent controversy, by showing that all previous studies are fundamentally flawed.

cond-mat.supr-con↗

arXiv1997

Numerical Investigation of the Dynamics of a Thin Film Type II Superconductor with and without Disorder

The equilibrium dynamics of a thin film type II superconductor with spherical geometry are investigated numerically in a simulation based on the lowest Landau level approximation to the time-dependent Ginzburg-Landau equation. Both the static and time-dependent density-density correlation functions of the superconducting order parameter have been investigated. As the temperature is lowered the correlation length, the length-scale over which the vortices have short-range crystalline order, increases but the introduction of quenched random disorder reduces this correlation length. We see no signs of a phase transition in either the pure or the disordered case. For the disordered system there is no evidence for the existence of a Bragg glass phase with quasi long-range correlations. The dynamics in both the pure and disordered systems is activated, and the barrier of the relaxation mechanism grows linearly with the correlation length. The self-diffusion time scale of the vortices was also measured and has the same temperature dependence as that of the longest time scales found in the time dependent density-density correlation function. The dominant relaxation mechanism observed is a change in orientation of a correlated region of size of the correlation length. A scaling argument is given to explain the value of the barrier exponent.

cond-mat.supr-con↗