Self-avoiding walk

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A self-avoiding walk (SAW) is a sequence of moves on a lattice which does not visit the same point more than once. A self-avoiding polygon (SAP) is a closed () self-avoiding walk on a lattice.

As such, SAWs are often used to model the real-life behaviour of chain-like entities such as solvents and polymers, whose physical volume prohibits multiple occupation of the same spatial point.

In computational physics a self-avoiding walk is a chain-like path in ℝ² or ℝ³ with a certain number of nodes, typically a fixed step length and has the imperative property that it doesn't cross itself or another walk. A system of self-avoiding walks satisfies the so called excluded volume condition.

A self-avoiding walk is interesting for simulations because its properties cannot be calculated analytically, thus it is very helpful to understand polymers, e.g. DNA molecules.

SAWs SAPs play a central role in the modelling of the topological and knot-theoretic behaviour of thread- and loop-like molecules such as proteins.

Calculating the number of self-avoiding walks in any given lattice is a common computational problem. There is currently no known formula for determining the number of self-avoiding walks, although there are rigorous methods for approximating them. ^[1]^[2]

[edit] Further reading

Madras, N.; Slade, G. (1996). The Self-Avoiding Walk. Birkhäuser. ISBN 978-0817638917.
Lawler, G. F. (1991). Intersections of Random Walks. Birkhäuser. ISBN 978-0817638924.