three dimensions [@HG94; @JvRR04; @ML88A]. Similary, the data are also consistent with estimates for the surface exponent $\gamma_s$; this is seen particularly in the scaling of the partition function (see equation ).

The paper is concluded with a few brief remarks and a summary in section \[section4\].

figure2-.tex

GAS Sampling of self-avoiding walks {#section2}
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The GAS algorithm is a generalisation of kinetic growth algorithms. It is designed to sample along weighted sequences in state space in such a way that the ratios of average weights of sequences ending in walks of length $n$ and $m$ are estimates of the ratio of the numbers of walks of lengths $n$ and $m$. In this section I show how to generalise this algorithm so that it can be used to estimate the number of walks of length $n$ and *energy* $m$. That is, the algorithm will be used to sample walks in the microcanonical ensemble.

Let $w=\LA \omega_0,\omega_1,\ldots,\omega_n\RA$ be a self-avoiding walk of length $n$ from its source vertex $\omega_0 =\vec{0}$ at the origin, to its terminal vertex $\omega_n$, giving $n$ steps $\LA \omega_{j-1},\omega_j\RA$ for $j=1,2,\ldots,n$. The walk $w$ may be made longer by adding a step $\LA \omega_n,\omega_{n+1}\RA$ to $\omega_n$, or 