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

Valence-shell double photoionization of alkaline-earth-metal atoms

We apply the convergent close-coupling formalism to describe direct double photoionization (DPI) of the valence n s2 shell of alkaline-earth-metal atoms: beryllium (n=2), magnesium (n=3), and calcium (n=4). We consider the range of photon energies below the onset of resonant and Auger ionization processes where the subvalent and core electrons can be treated as spectators. By comparing alkaline-earth-metal atoms with helium, we elucidate the role of the ground state and final ionized state correlations in DPI of various quasi-two-electron atoms

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

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

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 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

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

Disappearance of the de Almeida-Thouless line in six dimensions

We show that the Almeida-Thouless line in Ising spin glasses vanishes when their dimension d -> 6 as h_{AT}^2/T_c^2 = C(d-6)^4(1- T/T_c)^{d/2 - 1}, where C is a constant of order unity. An equivalent result which could be checked by simulations is given for the one-dimensional Ising spin glass with long-range interactions. It is shown that replica symmetry breaking also stops as d -> 6.Comment: Additional text and one figure adde

Non-equilibrium Phase-Ordering with a Global Conservation Law

In all dimensions, infinite-range Kawasaki spin exchange in a quenched Ising model leads to an asymptotic length-scale $L \sim (\rho t)^{1/2} \sim t^{1/3}$ at $T=0$ because the kinetic coefficient is renormalized by the broken-bond density, $\rho \sim L^{-1}$. For $T>0$, activated kinetics recovers the standard asymptotic growth-law, $L \sim t^{1/2}$. However, at all temperatures, infinite-range energy-transport is allowed by the spin-exchange dynamics. A better implementation of global conservation, the microcanonical Creutz algorithm, is well behaved and exhibits the standard non-conserved growth law, $L \sim t^{1/2}$, at all temperatures.Comment: 2 pages and 2 figures, uses epsf.st