Finite size effects in critical dynamics and the renormalization group

J. C. Niel, Jean Zinn‐Justin

Masuo Suzuki

Fisher's static finite-size scaling law is derived on the basis of the renormalization group theory and it is extended to dynamic critical phenomena in a finite system. This dynamic finite-size scaling law yields a cross-over effect with respect to the size and time-region. This effect is useful in analyzing computer simulations and also in studying the scaling property of the Kondo effect near the absolute zero temperature.

Joseph Rudnick, Hong Min Guo, David Jasnow

David Lancaster, Juan Jesus Ruiz-Lorenzo

Numerical simulations of the random phase sine–Gordon model suffer from strong finite size effects preventing the non-Gaussian log 2 r component of the spatial correlator from following the universal infinite volume prediction. We show that a finite size prediction based on perturbative renormalization group (RG) arguments agrees well with new high precision simulations for small coupling and close to the critical temperature.

Franz Wegner

J. A. Plascak, W. Figueiredo, B. C. S. Grandi

Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate critical behavior of model on infinite lattice is obtained through the exact computation of some thermal quantities of the model on finite clusters. In this work some of these methods are reviewed, namely the mean field renormalization group, the effective field renormalization group and the finite size scaling renormalization group procedures. Although special emphasis is given to the mean field renormalization group (since it has been, up to now, much more used to study a wide variety of different systems) a discussion of their potentialities and interrelations to other methods is also presented.