Poghosyan Vahagn ; Priezzhev Viacheslav ; Ruelle Philippe
We use the transfer matrix formalism for dimers proposed by Lieb, and generalize it to address the corresponding problem for arrow configurations (or trees) associated to dimer configurations through Temperley's correspondence. On a cylinder, the arrow configurations can be partitioned into sectors according to the number of non-contractible loops they contain. We show how Lieb's transfer matrix can be adapted in order to disentangle the various sectors and to compute the corresponding partition functions. In order to address the issue of Jordan cells, we introduce a new, extended transfer matrix, which not only keeps track of the positions of the dimers, but also propagates colors along the branches of the associated trees. We argue that this new matrix contains Jordan cells.
oai:noad.sci.am:136134
10.1088/1742-5468/2014/09/P09031
Journal of Statistical Mechanics: Theory and Experiment
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research ; Institute of Mechanics, Bulgarian Academy of Sciences ; Institute for Informatics and Automation Problems ; Institute for Research in Mathematics and Physics, Université catholique de Louvain
Armenia ; Russia ; Bulgaria ; Belgium
Apr 19, 2021
Apr 19, 2021
15
https://noad.sci.am/publication/149481
Edition name | Date |
---|---|
J G Brankov, Transfer matrix for spanning trees, webs and colored forests | Apr 19, 2021 |