The Stability of the Replica Symmetric State in Finite Dimensional Spin Glasses

According to the droplet picture of spin glasses, the low-temperature phase of spin glasses should be replica symmetric. However, analysis of the stability of this state suggested that it was unstable and this instability lends support to the Parisi replica symmetry breaking picture of spin glasses. The finite-size scaling functions in the critical region of spin glasses below T_c in dimensions greater than 6 can be determined and for them the replica symmetric solution is unstable order by order in perturbation theory. Nevertheless the exact solution can be shown to be replica-symmetric. It is suggested that a similar mechanism might apply in the low-temperature phase of spin glasses in less than six dimensions, but that a replica symmetry broken state might exist in more than six dimensions.Comment: 5 pages. Modified to include a paragraph on the relation of this work to that of Newman and Stei

Is the droplet theory for the Ising spin glass inconsistent with replica field theory?

Symmetry arguments are used to derive a set of exact identities between irreducible vertex functions for the replica symmetric field theory of the Ising spin glass in zero magnetic field. Their range of applicability spans from mean field to short ranged systems in physical dimensions. The replica symmetric theory is unstable for d>8, just like in mean field theory. For 6<d<8 and d<6 the resummation of an infinite number of terms is necessary to settle the problem. When d<8, these Ward-like identities must be used to distinguish an Almeida-Thouless line from the replica symmetric droplet phase.Comment: 4 pages. Accepted for publication in J.Phys.A. This is the accepted version with the following minor changes: one extra sentence in the abstract; footnote 2 slightly extended; last paragraph somewhat reformulate

Phase Ordering Kinetics with External Fields and Biased Initial Conditions

The late-time phase-ordering kinetics of the O(n) model for a non-conserved order parameter are considered for the case where the O(n) symmetry is broken by the initial conditions or by an external field. An approximate theoretical approach, based on a `gaussian closure' scheme, is developed, and results are obtained for the time-dependence of the mean order parameter, the pair correlation function, the autocorrelation function, and the density of topological defects [e.g. domain walls ($n=1$), or vortices ($n=2$)]. The results are in qualitative agreement with experiments on nematic films and related numerical simulations on the two-dimensional XY model with biased initial conditions.Comment: 35 pages, latex, no figure

Dynamics of Ordering of Heisenberg Spins with Torque --- Nonconserved Case. I

We study the dynamics of ordering of a nonconserved Heisenberg magnet. The dynamics consists of two parts --- an irreversible dissipation into a heat bath and a reversible precession induced by a torque due to the local molecular field. For quenches to zero temperature, we provide convincing arguments, both numerically (Langevin simulation) and analytically (approximate closure scheme due to Mazenko), that the torque is irrelevant at late times. We subject the Mazenko closure scheme to systematic numerical tests. Such an analysis, carried out for the first time on a vector order parameter, shows that the closure scheme performs respectably well. For quenches to $T_c$, we show, to ${\cal O}(\epsilon^2)$, that the torque is irrelevant at the Wilson-Fisher fixed point.Comment: 13 pages, REVTEX, and 19 .eps figures, compressed, Submitted to Phys. Rev.

Coarsening and Pinning in the Self-consistent Solution of Polymer Blends Phase-Separation Kinetics

We study analytically a continuum model for phase-separation in binary polymer blends based on the Flory-Huggins-De Gennes free energy, by means of the self-consistent large-$n$ limit approach. The model is solved for values of the parameters corresponding to the weak and strong segregation limits. For deep quenches we identify a complex structure of intermediate regimes and crossovers characterized by the existence of a time domain such that phase separation is pinned, followed by a preasymptotic regime which in the scalar case corresponds to surface diffusion. The duration of the pinning is analytically computed and diverges in the strong segregation limit. Eventually a late stage dynamics sets in, described by scaling laws and exponents analogous to those of the corresponding small molecule systems.Comment: 16 pages, 5 figures. Submitted to Phys. Rev.

Identification of the critical temperature from non-equilibrium time-dependent quantities

We present a new procedure able to identify and measure the critical temperature. This method is based on the divergence of the relaxation time approaching the critical point in quenches from infinite temperature. We introduce a dimensionless quantity that turns out to be time-independent at the critical temperature. The procedure does not need equilibration and allows for a relatively fast identification of the critical temperature. The method is first tested in the ferromagnetic Ising model and then applied to the one-dimensional Ising spin glass with power-law interactions. Here we always find a finite critical temperature also in presence of a uniform external field, in agreement with the mean-field picture for the low temperature phase of spin glasses.Comment: 6 pages, 10 figure

Phase Ordering Kinetics of One-Dimensional Non-Conserved Scalar Systems

We consider the phase-ordering kinetics of one-dimensional scalar systems. For attractive long-range ($r^{-(1+\sigma)}$) interactions with $\sigma>0$, ``Energy-Scaling'' arguments predict a growth-law of the average domain size $L \sim t^{1/(1+\sigma)}$ for all $\sigma >0$. Numerical results for $\sigma=0.5$, $1.0$, and $1.5$ demonstrate both scaling and the predicted growth laws. For purely short-range interactions, an approach of Nagai and Kawasaki is asymptotically exact. For this case, the equal-time correlations scale, but the time-derivative correlations break scaling. The short-range solution also applies to systems with long-range interactions when $\sigma \rightarrow \infty$, and in that limit the amplitude of the growth law is exactly calculated.Comment: 19 pages, RevTex 3.0, 8 FIGURES UPON REQUEST, 1549

The critical exponents of the two-dimensional Ising spin glass revisited: Exact Ground State Calculations and Monte Carlo Simulations

The critical exponents for $T\to0$ of the two-dimensional Ising spin glass model with Gaussian couplings are determined with the help of exact ground states for system sizes up to $L=50$ and by a Monte Carlo study of a pseudo-ferromagnetic order parameter. We obtain: for the stiffness exponent $y(=\theta)=-0.281\pm0.002$, for the magnetic exponent $\delta=1.48 \pm 0.01$ and for the chaos exponent $\zeta=1.05\pm0.05$. From Monte Carlo simulations we get the thermal exponent $\nu=3.6\pm0.2$. The scaling prediction $y=-1/\nu$ is fulfilled within the error bars, whereas there is a disagreement with the relation $y=1-\delta$.Comment: 8 pages RevTeX, 7 eps-figures include

Coarsening and persistence in a class of stochastic processes interpolating between the Ising and voter models

We study the dynamics of a class of two dimensional stochastic processes, depending on two parameters, which may be interpreted as two different temperatures, respectively associated to interfacial and to bulk noise. Special lines in the plane of parameters correspond to the Ising model, voter model and majority vote model. The dynamics of this class of models may be described formally in terms of reaction diffusion processes for a set of coalescing, annihilating, and branching random walkers. We use the freedom allowed by the space of parameters to measure, by numerical simulations, the persistence probability of a generic model in the low temperature phase, where the system coarsens. This probability is found to decay at large times as a power law with a seemingly constant exponent $\theta\approx 0.22$. We also discuss the connection between persistence and the nature of the interfaces between domains.Comment: Late

Replica field theory and renormalization group for the Ising spin glass in an external magnetic field

We use the generic replica symmetric cubic field-theory to study the transition of short range Ising spin glasses in a magnetic field around the upper critical dimension, d=6. A novel fixed-point is found, in addition to the well-known zero magnetic field fixed-point, from the application of the renormalization group. In the spin glass limit, n going to 0, this fixed-point governs the critical behaviour of a class of systems characterised by a single cubic interaction parameter. For this universality class, the spin glass susceptibility diverges at criticality, whereas the longitudinal mode remains massive. The third mode, the so-called anomalous one, however, behaves unusually, having a jump at criticality. The physical consequences of this unusual behaviour are discussed, and a comparison with the conventional de Almeida-Thouless scenario presented.Comment: 5 pages written in revtex4. Accepted for publication in Phys. Rev. Let