Nontrivial Polydispersity Exponents in Aggregation Models

We consider the scaling solutions of Smoluchowski's equation of irreversible aggregation, for a non gelling collision kernel. The scaling mass distribution f(s) diverges as s^{-tau} when s->0. tau is non trivial and could, until now, only be computed by numerical simulations. We develop here new general methods to obtain exact bounds and good approximations of $\tau$. For the specific kernel KdD(x,y)=(x^{1/D}+y^{1/D})^d, describing a mean-field model of particles moving in d dimensions and aggregating with conservation of ``mass'' s=R^D (R is the particle radius), perturbative and nonperturbative expansions are derived. For a general kernel, we find exact inequalities for tau and develop a variational approximation which is used to carry out the first systematic study of tau(d,D) for KdD. The agreement is excellent both with the expansions we derived and with existing numerical values. Finally, we discuss a possible application to 2d decaying turbulence.Comment: 16 pages (multicol.sty), 6 eps figures (uses epsfig), Minor corrections. Notations improved, as published in Phys. Rev. E 55, 546

Fluctuation-driven insulator-to-metal transition in an external magnetic field

We consider a model for a metal-insulator transition of correlated electrons in an external magnetic field. We find a broad region in interaction and magnetic field where metallic and insulating (fully magnetized) solutions coexist and the system undergoes a first-order metal-insulator transition. A global instability of the magnetically saturated solution precedes the local ones and is caused by collective fluctuations due to poles in electron-hole vertex functions.Comment: REVTeX 4 pages, 3 PS figure

Effects of in-chain and off-chain substitutions on spin fluctuations in the spin-Peierls compound CuGeO_3

The effect of in-chain and off-chain substitutions on 1D spin fluctuations in the spin-Peierls compound CuGeO_3 has been studied using Raman scattering in order to understand the interplay between defect induced states, enhanced spin-spin correlations and the ground state of low dimensional systems. In-chain and off-chain substitutions quench the spin-Peierls state and induce 3D antiferromagnetic order at T\leq 5 K. Consequently a suppression of a 1D gap-induced mode as well as a constant intensity of a spinon continuum are observed at low temperatures. A 3D two-magnon density of states now gradually extends to higher temperatures T\leq 60K compared with pure CuGeO_3. This effect is more pronounced in the case of off-chain substitutions (Si) for which a N\'eel state occurs over a larger substitution range, starting at very low concentrations. Besides, additional low energy excitations are induced. These effects, i.e. the shift of a dimensional crossover to higher temperatures are due to an enhancement of the spin-spin correlations induced by a small amount of substitutions. The results are compared with recent Monte Carlo studies on substituted spin ladders, pointing to a similar instability of coupled, dimerized spin chains and spin ladders upon substitution.Comment: 14 pages, 6 eps figures, to be published in PR

Dynamic Scaling in One-Dimensional Cluster-Cluster Aggregation

We study the dynamic scaling properties of an aggregation model in which particles obey both diffusive and driven ballistic dynamics. The diffusion constant and the velocity of a cluster of size $s$ follow $D(s) \sim s^\gamma$ and $v(s) \sim s^\delta$, respectively. We determine the dynamic exponent and the phase diagram for the asymptotic aggregation behavior in one dimension in the presence of mixed dynamics. The asymptotic dynamics is dominated by the process that has the largest dynamic exponent with a crossover that is located at $\delta = \gamma - 1$. The cluster size distributions scale similarly in all cases but the scaling function depends continuously on $\gamma$ and $\delta$. For the purely diffusive case the scaling function has a transition from exponential to algebraic behavior at small argument values as $\gamma$ changes sign whereas in the drift dominated case the scaling function decays always exponentially.Comment: 6 pages, 6 figures, RevTeX, submitted to Phys. Rev.