Real-space dynamic renormalization group. I. General formalism

Abstract

A general scheme is presented for applying real-space renormalization-group methods to dynamic critical phenomena. The method is based on mapping the time evolution operator for the initial variables onto a new operator acting on the block variables. The general formalism is discussed in the context of the kinetic Ising model. It is shown that all non-Markovian effects in the new operator can be eliminated if the renormalization-group transformation is taken to be the solution of a generalized eigenvalue equation. We show how to solve this equation perturbatively. The resulting transformation is such that the dynamics of the block spins is given by the slowest dynamic modes of the initial spins within a block.