Abstract
Kasteleyn's explicit result for the number of self-avoiding walks which completely fill a “Manhattan-oriented” plane square lattice is reanalyzed asymptotically. The number of N-step walks per lattice point is shown to vary as c N(M) ∼ Aμ N{1 + O( N -1+∈)} ( N → ∞, ∈ > 0) , where A, as well as μ is evaluated explicitly. This result is compared with the form c N ∼ AN αμ N ( N → ∞) , based on a numerical study of self-avoiding but non-filling walks on the same lattice.
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