Defect energy of infinite-component vector spin glasses

We compute numerically the zero temperature defect energy, Delta E, of the vector spin glass in the limit of an infinite number of spin components m, for a range of dimensions 2 <= d <= 5. Fitting to Delta E ~ L^theta, where L is the system size, we obtain: theta = -1.54 (d=2), theta = -1.04 (d=3), theta = -0.67 (d=4) and theta = -0.37 (d=5). These results show that the lower critical dimension, d_l (the dimension where theta changes sign), is significantly higher for m=infinity than for finite m (where 2 < d_l < 3).Comment: 4 pages, 5 figure

Spin glasses in the limit of an infinite number of spin components

We consider the spin glass model in which the number of spin components, m, is infinite. In the formulation of the problem appropriate for numerical calculations proposed by several authors, we show that the order parameter defined by the long-distance limit of the correlation functions is actually zero and there is only "quasi long range order" below the transition temperature. We also show that the spin glass transition temperature is zero in three dimensions.Comment: 9 pages, 13 figure

Survival of a diffusing particle in an expanding cage

We consider a Brownian particle, with diffusion constant D, moving inside an expanding d-dimensional sphere whose surface is an absorbing boundary for the particle. The sphere has initial radius L_0 and expands at a constant rate c. We calculate the joint probability density, p(r,t|r_0), that the particle survives until time t, and is at a distance r from the centre of the sphere, given that it started at a distance r_0 from the centre.Comment: 5 page

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

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.Comment: 4 pages, 6 figure

On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents

Finite-size scaling (FSS) is a standard technique for measuring scaling exponents in spin glasses. Here we present a critique of this approach, emphasizing the need for all length scales to be large compared to microscopic scales. In particular we show that the replacement, in FSS analyses, of the correlation length by its asymptotic scaling form can lead to apparently good scaling collapses with the wrong values of the scaling exponents.Comment: RevTeX, 5 page

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 of conserved vectorial systems with field-dependent mobility

The dynamics of phase-separation in conserved systems with an O(N) continuous symmetry is investigated in the presence of an order parameter dependent mobility M(\phi)=1-a \phi^2. The model is studied analytically in the framework of the large-N approximation and by numerical simulations of the N=2, N=3 and N=4 cases in d=2, for both critical and off-critical quenches. We show the existence of a new universality class for a=1 characterized by a growth law of the typical length L(t) ~ t^{1/z} with dynamical exponent z=6 as opposed to the usual value z=4 which is recovered for a<1.Comment: RevTeX, 8 pages, 13 figures, to be published in Phys. Rev.

Near-threshold behavior of positronium-antiproton scattering

Using the convergent close-coupling theory we study the threshold behavior of cross sections for positronium (Ps) of energy E scattering on antiprotons. In the case of Ps(1s) elastic scattering, simple power laws are observed for all partial waves studied. The partial-wave summed cross section is nearly constant, and dominates the antihydrogen formation cross section at all considered energies, even though the latter is exothermic and behaves as 1/E1/2. For Ps(2s), oscillations spanning orders of magnitude on top of the 1/E behavior are found in the elastic and quasielastic cross sections. The antihydrogen formation is influenced by dipole-supported resonances below the threshold of inelastic processes. Resonance energies form a geometric progression relative to the threshold. The exothermic antihydrogen formation cross sections behave as 1/E at low energies, but are oscillation free. We demonstrate that all these rich features are reproduced by the threshold theory developed by Gailiti

Domain-Wall Energies and Magnetization of the Two-Dimensional Random-Bond Ising Model

We study ground-state properties of the two-dimensional random-bond Ising model with couplings having a concentration $p\in[0,1]$ of antiferromagnetic and $(1-p)$ of ferromagnetic bonds. We apply an exact matching algorithm which enables us the study of systems with linear dimension $L$ up to 700. We study the behavior of the domain-wall energies and of the magnetization. We find that the paramagnet-ferromagnet transition occurs at $p_c \sim 0.103$ compared to the concentration $p_n\sim 0.109$ at the Nishimory point, which means that the phase diagram of the model exhibits a reentrance. Furthermore, we find no indications for an (intermediate) spin-glass ordering at finite temperature.Comment: 7 pages, 12 figures, revTe