A study of cross sections for excitation of pseudostates

Using the electron-hydrogen scattering Temkin-Poet model we investigate the behavior of the cross sections for excitation of all of the states used in the convergent close-coupling (CCC) formalism. In the triplet channel, it is found that the cross section for exciting the positive-energy states is approximately zero near-threshold and remains so until a further energy, equal to the energy of the state, is added to the system. This is consistent with the step-function hypothesis [Bray, Phys. Rev. Lett. {\bf 78} 4721 (1997)] and inconsistent with the expectations of Bencze and Chandler [Phys. Rev. A {\bf 59} 3129 (1999)]. Furthermore, we compare the results of the CCC-calculated triplet and singlet single differential cross sections with the recent benchmark results of Baertschy et al. [Phys. Rev. A (to be published)], and find consistent agreement.Comment: Four pages, 5 figure

Phase Ordering Dynamics of the O(n) Model - Exact Predictions and Numerical Results

We consider the pair correlation functions of both the order parameter field and its square for phase ordering in the $O(n)$ model with nonconserved order parameter, in spatial dimension $2\le d\le 3$ and spin dimension $1\le n\le d$. We calculate, in the scaling limit, the exact short-distance singularities of these correlation functions and compare these predictions to numerical simulations. Our results suggest that the scaling hypothesis does not hold for the $d=2$ $O(2)$ model. Figures (23) are available on request - email [email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2

On the number of metastable states in spin glasses

In this letter, we show that the formulae of Bray and Moore for the average logarithm of the number of metastable states in spin glasses can be obtained by calculating the partition function with $m$ coupled replicas with the symmetry among these explicitly broken according to a generalization of the `two-group' ansatz. This equivalence allows us to find solutions of the BM equations where the lower `band-edge' free energy equals the standard static free energy. We present these results for the Sherrington-Kirkpatrick model, but we expect them to apply to all mean-field spin glasses.Comment: 6 pages, LaTeX, no figures. Postscript directly available http://chimera.roma1.infn.it/index_papers_complex.htm

Corrections to Scaling in the Phase-Ordering Dynamics of a Vector Order Parameter

Corrections to scaling, associated with deviations of the order parameter from the scaling morphology in the initial state, are studied for systems with O(n) symmetry at zero temperature in phase-ordering kinetics. Including corrections to scaling, the equal-time pair correlation function has the form C(r,t) = f_0(r/L) + L^{-omega} f_1(r/L) + ..., where L is the coarsening length scale. The correction-to-scaling exponent, omega, and the correction-to-scaling function, f_1(x), are calculated for both nonconserved and conserved order parameter systems using the approximate Gaussian closure theory of Mazenko. In general, omega is a non-trivial exponent which depends on both the dimensionality, d, of the system and the number of components, n, of the order parameter. Corrections to scaling are also calculated for the nonconserved 1-d XY model, where an exact solution is possible.Comment: REVTeX, 20 pages, 2 figure

Velocity Distribution of Topological Defects in Phase-Ordering Systems

The distribution of interface (domain-wall) velocities ${\bf v}$ in a phase-ordering system is considered. Heuristic scaling arguments based on the disappearance of small domains lead to a power-law tail, $P_v(v) \sim v^{-p}$ for large v, in the distribution of $v \equiv |{\bf v}|$. The exponent p is given by $p = 2+d/(z-1)$, where d is the space dimension and 1/z is the growth exponent, i.e. z=2 for nonconserved (model A) dynamics and z=3 for the conserved case (model B). The nonconserved result is exemplified by an approximate calculation of the full distribution using a gaussian closure scheme. The heuristic arguments are readily generalized to conserved case (model B). The nonconserved result is exemplified by an approximate calculation of the full distribution using a gaussian closure scheme. The heuristic arguments are readily generalized to systems described by a vector order parameter.Comment: 5 pages, Revtex, no figures, minor revisions and updates, to appear in Physical Review E (May 1, 1997

Vortex annihilation in the ordering kinetics of the O(2) model

The vortex-vortex and vortex-antivortex correlation functions are determined for the two-dimensional O(2) model undergoing phase ordering. We find reasonably good agreement with simulation results for the vortex-vortex correlation function where there is a short-scaled distance depletion zone due to the repulsion of like-signed vortices. The vortex-antivortex correlation function agrees well with simulation results for intermediate and long-scaled distances. At short-scaled distances the simulations show a depletion zone not seen in the theory.Comment: 28 pages, REVTeX, submitted to Phys. Rev.

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

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

Corrections to Scaling in Phase-Ordering Kinetics

The leading correction to scaling associated with departures of the initial condition from the scaling morphology is determined for some soluble models of phase-ordering kinetics. The result for the pair correlation function has the form C(r,t) = f_0(r/L) + L^{-\omega} f_1(r/L) + ..., where L is a characteristic length scale extracted from the energy. The correction-to-scaling exponent \omega has the value \omega=4 for the d=1 Glauber model, the n-vector model with n=\infty, and the approximate theory of Ohta, Jasnow and Kawasaki. For the approximate Mazenko theory, however, \omega has a non-trivial value: omega = 3.8836... for d=2, and \omega = 3.9030... for d=3. The correction-to-scaling functions f_1(x) are also calculated.Comment: REVTEX, 7 pages, two figures, needs epsf.sty and multicol.st

Evidence for existence of many pure ground states in 3d ±J\pm J Spin Glasses

Ground states of 3d EA Ising spin glasses are calculated for sizes up to $14^3$ using a combination of genetic algorithms and cluster-exact approximation . The distribution $P(|q|)$ of overlaps is calculated. For increasing size the width of $P(|q|)$ converges to a nonzero value, indicating that many pure ground states exist for short range Ising spin glasses.Comment: 4 pages, 3 figures, 2 tables, 16 reference