Finite-size scaling analysis of generalized mean-field theories

Scaling and mean-field theories applied to polymer brushes.

Analysis of the osmotic pressures of aqueous poly(ethylene glycol) solutions indicates a power-law behavior in the range of volume fractions from 0.08–0.12 to 0.33 or higher, for polymers with average molecular masses in the range 1500– 4000 Da. The exponent of the power law is closer to a value of 2, which is predicted by mean-field theory, than to the value of 5/4, which is predicted by scali...

Finite - size scaling at the dynamical transition of the mean - field 10 - state Potts glass

We use Monte Carlo simulations to study the static and dynamical properties of a Potts glass with infinite range Gaussian distributed exchange interactions for a broad range of temperature and system size up to N = 2560 spins. The results are compatible with a critical divergence of the relaxation time τ at the theoretically predicted dynamical transition temperature TD, τ ∝ (T−TD) −∆ with ∆ ≈ ...

Finite - size scaling and the deconfinement transition in gauge theories

We introduce a new method for determining the critical indices of the deconfinement transition in gauge theories. The method is based on the finite size scaling behavior of the expectation value of simple lattice operators, such as the plaquette. We test the method for the case of SU (3) pure gauge theory in (2 + 1) dimensions and obtain a precise determination of the critical index ν, in agree...

Finite-size critical scaling in Ising spin glasses in the mean-field regime.

We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one...

Hierarchical Mean-field Theories