Renormalization group theory, the epsilon expansion and Ken Wilson as I knew him

The tasks posed for renormalization group theory (RGT) within statistical physics by critical phenomena theory in the 1960's are set out briefly in contradistinction to quantum field theory (QFT), which was the origin for Ken Wilson's concerns. Kadanoff's 1966 block spin scaling picture and its difficulties are presented; Wilson's early vision of flows is described from the author's perspective. How Wilson's subsequent breakthrough ideas, published in 1971, led to the epsilon expansion and the resulting clarity is related. Concluding sections complete the general picture of flows in a space of Hamiltonians, universality and scaling. The article represents a 40% condensation (but with added items) of an earlier account: Rev. Mod. Phys.70, 653–681 (1998).

SINGLE INTERFACE GROWTH: FLUCTUATIONS AND THE CORRELATION LENGTH

Growth behavior of interfaces is usually described by a power-law of the growth in time of the interface width. This general scaling picture is an average behavior description, which may not be valid when only a finite number of interfaces is considered. In this work we study theoretically and experimentally the growth behavior of single interfaces and show that the growth of the interface width always exhibits a non-monotonic, fluctuating behavior. We study numerically the Quenched-noise Kardar-Parisi-Zhang (QKPZ) equation, using different noise distributions, and show that this behavior results from competing mechanisms of normal growth and surface tension forces in this equation. We define a new measure of the interface width fluctuations and present a way to extract the correlation length of the interface from these fluctuations.