Scaling of self-avoiding walks in high dimensions
نویسندگان
چکیده
We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte Carlo simulations up to length N = 16 384, providing the first such results in dimensions d > 4 on which we concentrate our analysis. We analyse the scaling behaviour of the partition function and the statistics of nearest-neighbour contacts, as well as the average geometric size of the walks, and compare our results to 1/d-expansions and to excellent rigorous bounds that exist. In particular, we obtain precise values for the connective constants, μ5 = 8.838 544(3), μ6 = 10.878 094(4), μ7 = 12.902 817(3), μ8 = 14.919 257(2) and give a revised estimate of μ4 = 6.774 043(5). All of these are by at least one order of magnitude more accurate than those previously given (from other approaches in d > 4 and all approaches in d = 4). Our results are consistent with most theoretical predictions, though in d = 5 we find clear evidence of anomalous N−1/2-corrections for the scaling of the geometric size of the walks, which we understand as a non-analytic correction to scaling of the general form N(4−d)/2 (not present in pure Gaussian random walks). PACS numbers: 05.50.+q, 05.70.Fh, 61.41.+e, 64.60.-i
منابع مشابه
High - precision determination of the criticalexponent for self - avoiding
We compute the exponent for self-avoiding walks in three dimensions. We get = 1:1575 0:0006 in agreement with renormalization-group predictions. Earlier Monte Carlo and exact-enumeration determinations are now seen to be biased by corrections to scaling.
متن کاملWalking on fractals: diffusion and self-avoiding walks on percolation clusters
We consider random walks (RWs) and self-avoiding walks (SAWs) on disordered lattices directly at the percolation threshold. Applying numerical simulations, we study the scaling behavior of the models on the incipient percolation cluster in space dimensions d = 2, 3, 4. Our analysis yields estimates of universal exponents, governing the scaling laws for configurational properties of RWs and SAWs...
متن کاملScaling of Self-Avoiding Walks and Self-Avoiding Trails in Three Dimensions
Motivated by recent claims of a proof that the length scale exponent for the end-to-end distance scaling of self-avoiding walks is precisely 7/12 = 0.5833 . . ., we present results of large-scale simulations of self-avoiding walks and self-avoiding trails with repulsive contact interactions on the hypercubic lattice. We find no evidence to support this claim; our estimate ν = 0.5874(2) is in ac...
متن کاملCritical Behaviour of Self-avoiding Walk in Five or More Dimensions
We use the lace expansion to prove that in five or more dimensions the standard self-avoiding walk on the hypercubic (integer) lattice behaves in many respects like the simple random walk. In particular, it is shown that the leading asymptotic behaviour of the number of «-step self-avoiding walks is purely exponential, that the mean square displacement is asymptotically linear in the number of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001