Geometric Explanation of Anomalous Finite-Size Scaling in High Dimensions

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

Finite Size Scaling

We study the Bose-Einstein condensation phase transition in a weakly interacting gas through a perturbative analysis of finite systems. In both the grand canonical and the canonical ensembles, perturbation theory suffers from infrared divergences and cannot directly determine the transition temperature in the thermodynamic limit. However, in conjunction with finite size scaling, perturbation th...

Finite-Size Scaling in Percolation

This work is a detailed study of the phase transition in percolation, in particular of the question of finite-size scaling: Namely, how does the critical transition behavior emerge from the behavior of large, finite systems? Our results rigorously locate the proper window in which to do critical computation and establish features of the phase transition. This work is a finite-dimensional analog...

Finite size corrections to scaling in high Reynoldsnumber

We study analytically and numerically the corrections to scaling in turbulence which arise due to nite size eeects as anisotropic forcing or boundary conditions at large scales. We nd that the deviations m from the classical Kol-mogorov scaling m = m=3 of the velocity moments hju(k)j m i / k ?m decrease like m (Re) = c m Re ?3=10. If, on the contrary, anomalous scaling in the inertial subrange ...

Finite size corrections to scaling in high Reynolds number turbulence.

We study analytically and numerically the corrections to scaling in turbulence which arise due to the finite ratio of the outer scale L of turbulence to the viscous scale η, i.e., they are due to finite size effects as anisotropic forcing or boundary conditions at large scales. We find that the deviations δζm from the classical Kolmogorov scaling ζm = m/3 of the velocity moments 〈|u(k)|m〉 ∝ km ...