Critical scaling in random-field systems: 2 or 3 independent exponents?

Critical percolation in high dimensions: critical exponents, finite size scaling and random walks

ON QUASILINEAR ELLIPTIC SYSTEMS INVOLVING MULTIPLE CRITICAL EXPONENTS

In this paper, we consider the existence of a non-trivial weaksolution to a quasilinear elliptic system involving critical Hardyexponents. The main issue of the paper is to understand thebehavior of these Palais-Smale sequences. Indeed, the principaldifficulty here is that there is an asymptotic competition betweenthe energy functional carried by the critical nonlinearities. Thenby the variatio...

M ar 1 99 3 Critical Exponents of the Three Dimensional Random Field Ising Model

The phase transition of the three–dimensional random field Ising model with a discrete (±h) field distribution is investigated by extensive Monte Carlo simulations. Values of the critical exponents for the correlation length, specific heat, susceptibility, disconnected susceptibility and magnetization are determined simultaneously via finite size scaling. While the exponents for the magnetizati...

Further scaling exponents of random walks in random sceneries

Completing previous results, we construct, for every 1/2 6 s 6 1, explicit examples of nearest neighbour random walks on the nonnegative integer line such that s is the scaling exponent of the associated random walk in random scenery for square integrable i.i.d. sceneries. We use coupling techniques to compare the distributions of the local times of such random walks.

Finite-size scaling and critical exponents in critical relaxation.

We simulate the critical relaxation process of the two-dimensional Ising model with the initial state both completely disordered or completely ordered. Results of a new method to measure both the dynamic and static critical exponents are reported, based on the finite size scaling for the dynamics at the early time. From the time-dependent Binder cumulant, the dynamical exponent z is extracted i...