Renormalisation of the 'true' self-avoiding walk

Obukhov, S P; Peliti, Luca

doi:10.1088/0305-4470/16/5/004

Cited by 66 publications

(41 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Sometimes arguments which link the evolution equations which define the model to the geometrical properties of the outcoming aggregate have appeared [4][5][6][7][8]. Methods which are strictly related to the renormalization group have met with some success in the particular case of growing linear aggregates, which may be produced by processes described as random walks with memory [9][10][11][12][13]. In this case also Flory-like arguments have found some applicability [14,15].…”

Section: Introductionmentioning

confidence: 99%

Path integral approach to birth-death processes on a lattice

Peliti¹

1985

J. Phys. France

590

742

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Path integral approach to birth-death processes on a lattice

Peliti¹

1985

J. Phys. France

590

742

View full text Add to dashboard Cite

show abstract

“…Like Anderson localization, d = 2 is a critical dimension for the true self-avoiding walk. However in this case the RG flows [22,23] are to free random walks for d ≥ 2, and to a non-trivial stable fixed point for d < 2, while for Anderson localization we expect to find a non-trivial unstable fixed point for d > 2. This suggests that the two problems are related by a change of sign of the interaction.…”

Section: Summary and Further Remarksmentioning

confidence: 86%

“…This suggests that the two problems are related by a change of sign of the interaction. However the analysis of Peliti and Obukhov [23] shows that for history-dependent random walks there are in fact three coupling constants which are potentially important near d = 2. An attempt to fit the walks on the 2d Manhattan lattice into this picture was made in Ref.…”

Section: Summary and Further Remarksmentioning

confidence: 99%

Quantum Network Models and Classical Localization Problems

Cardy¹

2010

Int. J. Mod. Phys. B

View full text Add to dashboard Cite

A review is given of quantum network models in class C which, on a suitable 2d lattice, describe the spin quantum Hall plateau transition. On a general class of graphs, however, many observables of such models can be mapped to those of a classical walk in a random environment, thus relating questions of quantum and classical localization. In many cases it is possible to make rigorous statements about the latter through the relation to associated percolation problems, in both two and three dimensions.

show abstract

“…Our model seems to be related to yet another model of the self-avoiding walk, introduced by Amit et al [18], where the walker tries to avoid lattice sites that it has already visited. Renormalization-group arguments show that for such a model the critical dimension equals to 2 and the logarithmic corrections are present [18,19] in the critical dimension. It is likely that, at the coarse-grained level, our model is described by the same field theory as the model of Amit et al Its di-rect applicability to search strategies is rather limited but our model might indicate that the very dimension of the search space plays an important role.…”

Section: Final Remarksmentioning

confidence: 99%

Diffusive behavior of a greedy traveling salesman

Lipowski

Lipowska

2011

Phys. Rev. E

View full text Add to dashboard Cite

Using Monte Carlo simulations we examine the diffusive properties of the greedy algorithm in the d-dimensional traveling salesman problem. Our results show that for d = 3 and 4 the average squared distance from the origin r 2 is proportional to the number of steps t. In the d = 2 case such a scaling is modified with some logarithmic corrections, which might suggest that d = 2 is the critical dimension of the problem. The distribution of lengths also shows marked differences between d = 2 and d > 2 versions. A simple strategy adopted by the salesman might resemble strategies chosen by some foraging and hunting animals, for which anomalous diffusive behavior has recently been reported and interpreted in terms of Lévy flights. Our results suggest that broad and Lévy-like distributions in such systems might appear due to dimension-dependent properties of a search space.

show abstract

Renormalisation of the 'true' self-avoiding walk

Cited by 66 publications

References 1 publication

Path integral approach to birth-death processes on a lattice

Path integral approach to birth-death processes on a lattice

Quantum Network Models and Classical Localization Problems

Diffusive behavior of a greedy traveling salesman

Contact Info

Product

Resources

About