Object

Title: Transfer matrix for spanning trees, webs and colored forests

Author:

Brankov Jovan

Type:

Article

Co-author(s) :

Poghosyan Vahagn ; Priezzhev Viacheslav ; Ruelle Philippe

Abstract:

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.

Date submitted:

16.05.2014

Date accepted:

29.07.2014

Date of publication:

30.09.2014

Identifier:

oai:noad.sci.am:136134

DOI:

10.1088/1742-5468/2014/09/P09031

ISSN:

1742-5468

Language:

english

Journal or Publication Title:

Journal of Statistical Mechanics: Theory and Experiment

Volume:

2014

URL:


Additional Information:

philippe.ruelle@uclouvain.be

Affiliation:

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

Country:

Armenia ; Russia ; Bulgaria ; Belgium

Indexing:

Scopus

Object collections:

Last modified:

Apr 19, 2021

In our library since:

Apr 19, 2021

Number of object content hits:

4

All available object's versions:

https://noad.sci.am/publication/149481

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