Search for a Book
HELP US TO HELP YOU Add a new Book


Lectures on SelfAvoiding Walks

Language: 



Author:  Roland Bauerschmidt, Hugo DuminilCopin, Jesse Goodman, Gordon 
















Description 
These lecture notes provide a rapid introduction to a number of rigorous results on selfavoiding walks, with emphasis on the critical behaviour. Following an introductory overview of the central problems, an account is given of the HammersleyWelsh bound on the number of selfavoiding walks and its consequences for the growth rates of bridges and selfavoiding polygons. A detailed proof that the connective constant on the hexagonal lattice equals $\sqrt{2 \sqrt{2}}$ is then provided. The lace expansion for selfavoiding walks is described, and its use in understanding the critical behaviour in dimensions $d>4$ is discussed. Functional integral representations of the selfavoiding walk model are discussed and developed, and their use in a renormalisation group analysis in dimension 4 is sketched. Problems and solutions from tutorials are included. 

Similar Books 



Home  Authors  About  Contact Us  Email
Copyright © 20022013 FreeScience.info.
Best viewed with Mozilla 1.X 1024x768
free scientific books
