Dynamics of roughening and growth of two-dimensional self-avoiding walks

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Abstract
The one-dimensional surface of a two-dimensional lattice fluid is simulated by a method producing self-avoiding walks of varying lengths. Below the critical temperature, the surface width varies as the square root of the surface length in equilibrium, and at the critical point it varies as (time)1/3. Above the critical temperature, the width and the length of the surface increases initially as (time)1/2, whereas finally the "surface" fills the whole lattice. If, instead, we start above the critical point from a small ring, its squared radius of gyration and its length increase initially as (time)2/3. At the critical point, this growth from a small ring gives an average radius proportional to (length)0.75, as for self-avoiding walks.

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