Scaling in condensed matter physics: I. Finite-size effects in equilibrium critical phenomena. II. Dynamical growth of interfaces.

摘要

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 re-examined 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 Ising-like system is computed to one-loop 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.