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International audience; It has been known for a long time that the kinetics of diffusion-limited reactions can be quantified by the time needed for a diffusing molecule to reach a target: the first-passage time (FPT). So far the general determination of the mean first-passage time to a target in confinement has left aside aging media, such as glassy materials, cellular media, or cold atoms in optical lattices. Here we consider general non-Markovian scale-invariant diffusion processes, which model a broad class of transport processes of molecules in aging media, and demonstrate that all the moments of the FPT obey universal scalings with the confining volume with nontrivial exponents. Our analysis shows that a nonlinear scaling with the volume of the mean FPT, which quantities the mean reaction time, is the hallmark of aging and provides a general tool to quantify its impact on reaction kinetics in confinement.

The scaling function of the two-dimensional Ising model on the square and triangular lattices is obtained numerically via Baxter's variational corner transfer-matrix approach. The use of Aharony-Fisher nonlinear scaling variables allowed us to perform calculations sufficiently away from the critical point and to confirm all predictions of the scaling and universality hypotheses. Our results are in excellent agreement with quantum field theory calculations of Fonseca and Zamolodchikov as well as with many previously known exact and numerical calculations, including susceptibility results by Barouch, McCoy, Tracy, and Wu.

We study the diffusion of polymers through quenched short-range correlated random media by renormalization group (RG) methods, which allow us to derive universal predictions in the limit of long chains and weak disorder. We take local quenched random potentials with second momentv and the excluded-volume interactionu of the chain segments into account. We show that our model contains the relevant features of polymer diffusion in random media in the RG sense if we focus on the local entropic effects rather than on the topological constraints of a quenched random medium. The dynamic generating functional and the general structure of its perturbation expansion inu andv are derived. The distribution functions for the center-of-mass motion and the internal modes of one chain and for the correlation of the center of mass motions of two chains are calculated to one-loop order. The results allow for sufficient cross-checks to have trust in the one-loop renormalizability of the model. The general structure as well as the one-loop results of the integrated RG flow of the parameters are discussed. Universal results can be found for the effective static interactionw≔u−v≥0 and for small effective disorder coupling\(\bar v(l)\) on the intermediate length scalel. As a first physical prediction from our analysis, we determine the general nonlinear scaling form of the chain diffusion constant and evaluate it explicitly as Open image in new window for\(\bar v(l) \ll 1\).

The reliability of the hynothesis that two nonlinear scaling fieles and satisfy and , which is adopted in the theory of analytic correction to scaling due to nonlinearity of scaling fields, is investigated. It is shown that this hypothesis is a good one only when we take some suitable approximations under the quasi-asymptotic condition, even though ignore all the irrelevant variables, so that we can adopt it as a hypothesis in the theory with reservations. The third possible source for correction to scaling, the nonlinearity of order parameter, is also pointed out in addition to the source of the irrelevant variables and of the nonlinearity of scaling fields.

A selection of recent work by various authors concerning spin 1 2 ; Ising modls with pair couplings is reviewed. Topics addressed include: the universality of corrections-to-scaling and nonlinear scaling fields in planar Ising models; aspects of many-particle correlation functions; the testing and verification of scaling hypotheses for local magnetizations in the presence of walls and boundaries, including the singular nature of the critical region scaling functions and the decay of the influence of a far wall; a soluble model of a surface roughening transition; nonuniversal critical effects of one-dimensional perturbations in planar Ising models; the effects of spatially anisotropic further neighbor interactions, in particular ANNNI models in d 2 dimensions and soluble mock ANNNI models in 2 and 3 dimensions.