Scaling in Condensed Matter Physics: I. Finite  Effects in Equilibrium Critical Phenomena. II. Dynamical Growth of Interfaces.
Abstract
This thesis consists of two parts. Part I deals with critical phenomena in a finite system. The so called finite size scaling (FSS) theory is reexamined within the context of field theoretical renormalization group. Problems a computer simulator might encounter because of the finite size are addressed. The finite size scaling function for the specific heat of an Isinglike system is computed to oneloop order. It is shown that the conventional FSS is broken when spatial dimension is equal or beyond the upper critical dimension. A new proposal for finite size scaling due to Privman and Fisher is verified using renormalization group techniques and possible extensions of the new FSS to surface problems are discussed. In part II of the thesis we investigate, using computer simulation techniques, the dynamics of an interfacial growth instability. Evidence for a scaling regime in the growth is presented. It is found that the power spectrum of the interface shape evolves according to a scaling rule. Various growth exponents are obtained from the simulations and a possible relationship between them is discussed. The growth shows some degree of universality in that the exponents are independent of details of the system. Two different models are investigated and found that they belong to different universality classes.
 Publication:

Ph.D. Thesis
 Pub Date:
 1987
 Bibcode:
 1987PhDT........31G
 Keywords:

 Physics: Condensed Matter, Physics: Astronomy and Astrophysics