Counting in Lattices: Combinatorial Problems from Statistical Mechanics

@techreport{citeulike:2175794, abstract = {In this thesis we consider two classical combinatorial problems arising in statistical mechanics: counting matchings and self-avoiding walks in lattice graphs. The first problem arises in the study of the thermodynamical properties of monomers and dimers (diatomic molecules) in crystals. Fisher, Kasteleyn and Temperley discovered an elegant technique to exactly count the number of perfect matchings in two dimensional lattices, but it is not applicable for matchings of arbitrary size, or in...}, address = {Berkeley, CA}, author = {Randall, Dana }, citeulike-article-id = {2175794}, comment = {* MCMC algorithm for generating self-avoiding walks (also had a follow up paper)}, keywords = {combinatorics, saw}, number = {TR-94-055}, posted-at = {2007-12-27 21:21:32}, priority = {2}, title = {Counting in Lattices: Combinatorial Problems from Statistical Mechanics}, url = {http://citeseer.ist.psu.edu/randall94counting.html}, year = {1994} }

TY - RPRT ID - citeulike:2175794 L3 - citeulike-article-id:2175794 TI - Counting in Lattices: Combinatorial Problems from Statistical Mechanics IS - TR-94-055 AD - Berkeley, CA N2 - In this thesis we consider two classical combinatorial problems arising in statistical mechanics: counting matchings and self-avoiding walks in lattice graphs. The first problem arises in the study of the thermodynamical properties of monomers and dimers (diatomic molecules) in crystals. Fisher, Kasteleyn and Temperley discovered an elegant technique to exactly count the number of perfect matchings in two dimensional lattices, but it is not applicable for matchings of arbitrary size, or in... KW - combinatorics KW - saw N1 - * MCMC algorithm for generating self-avoiding walks (also had a follow up paper) AU - Randall, Dana PY - 1994/// UR - http://citeseer.ist.psu.edu/randall94counting.html ER -