DIMERS ON TWO- AND THREE-DIMENSIONAL LATTICES: SHIFT OPERATOR MATRIX SOLUTION.

We use the shift operator matrix (SOM) method developed by McQuistan and Hock to obtain the dimer occupational degeneracies for a three-dimensional L×M×Nlattice. The solution is given in terms of the shift operator, R, which reduces size Nof the lattice by one unit, and the annihilation operators, U, Vand W, of dimers parallel to the L-, M-, and N-axes, respectively. We show that the factorization observed by McQuistan and Hock for monomers distributed on the planar lattice is possible for dimers, and the degeneracy is obtained as a solution of an eigenvalue problem. In particular, it is interesting to note that, as in the monomer case, R- J plays the role of an eigenvalue operator of a matrix which is the Hadamard product of two matrices, one depending on W, and the other on U and V. The matrix depending on W it itself the Kronecker product of order LM of a 2 × 2 matrix. The matrix depending on Uand Vhas an interesting fractal-like structure, which may be used to reduce the complexity of the problem. Our previous work done with dimers having orientational dependent activities on planar lattices, 1 XM×N, was possible by considering only one lattice size at a time, M=2,3,4 or 5. The major advantage of the SOM method is to provide a general expression valid for any M and L.

Main Author: Phares, Alain J.
Other Authors: Wunderlich, Francis J.
Language: English
Published: 1988
Online Access: http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:179427
PID vudl:179427
id vudl:179427
modeltype_str_mv vudl-system:CoreModel
vudl-system:CollectionModel
vudl-system:ResourceCollection
datastream_str_mv DC
PARENT-QUERY
PARENT-LIST-RAW
PARENT-LIST
MEMBER-QUERY
MEMBER-LIST-RAW
LEGACY-METS
LICENSE
AGENTS
PROCESS-MD
THUMBNAIL
STRUCTMAP
RELS-EXT
hierarchytype
sequence_vudl_179402_str 0000000009
has_order_str no
hierarchy_top_id vudl:171664
hierarchy_top_title Villanova Digital Collection
hierarchy_parent_id vudl:179402
hierarchy_parent_title Wunderlich Francis J
hierarchy_sequence 0000000009
hierarchy_first_parent_id_str vudl:179427
hierarchy_sequence_sort_str 0000000009
hierarchy_all_parents_str_mv vudl:171664
vudl:172968
vudl:179402
first_indexed 2014-01-11T23:15:38Z
last_indexed 2014-01-11T23:15:38Z
recordtype vudl
fullrecord <root> <url> http://digital.library.villanova.edu/files/vudl:179427/DC </url> <thumbnail> http://digital.library.villanova.edu/files/vudl:179427/THUMBNAIL </thumbnail> </root>
spelling
institution Villanova University
collection Digital Library
language English
dc_source_str_mv Physics Letter A, Volume 130, number 6, 7, 1988.
author Phares, Alain J.
author_s Phares, Alain J.
spellingShingle Phares, Alain J.
DIMERS ON TWO- AND THREE-DIMENSIONAL LATTICES: SHIFT OPERATOR MATRIX SOLUTION.
author-letter Phares, Alain J.
author_sort_str Phares, Alain J.
author2 Wunderlich, Francis J.
author2Str Wunderlich, Francis J.
dc_title_str DIMERS ON TWO- AND THREE-DIMENSIONAL LATTICES: SHIFT OPERATOR MATRIX SOLUTION.
title DIMERS ON TWO- AND THREE-DIMENSIONAL LATTICES: SHIFT OPERATOR MATRIX SOLUTION.
title_short DIMERS ON TWO- AND THREE-DIMENSIONAL LATTICES: SHIFT OPERATOR MATRIX SOLUTION.
title_full DIMERS ON TWO- AND THREE-DIMENSIONAL LATTICES: SHIFT OPERATOR MATRIX SOLUTION.
title_fullStr DIMERS ON TWO- AND THREE-DIMENSIONAL LATTICES: SHIFT OPERATOR MATRIX SOLUTION.
title_full_unstemmed DIMERS ON TWO- AND THREE-DIMENSIONAL LATTICES: SHIFT OPERATOR MATRIX SOLUTION.
collection_title_sort_str dimers on two- and three-dimensional lattices: shift operator matrix solution.
title_sort dimers on two- and three-dimensional lattices: shift operator matrix solution.
description We use the shift operator matrix (SOM) method developed by McQuistan and Hock to obtain the dimer occupational degeneracies for a three-dimensional L×M×Nlattice. The solution is given in terms of the shift operator, R, which reduces size Nof the lattice by one unit, and the annihilation operators, U, Vand W, of dimers parallel to the L-, M-, and N-axes, respectively. We show that the factorization observed by McQuistan and Hock for monomers distributed on the planar lattice is possible for dimers, and the degeneracy is obtained as a solution of an eigenvalue problem. In particular, it is interesting to note that, as in the monomer case, R- J plays the role of an eigenvalue operator of a matrix which is the Hadamard product of two matrices, one depending on W, and the other on U and V. The matrix depending on W it itself the Kronecker product of order LM of a 2 × 2 matrix. The matrix depending on Uand Vhas an interesting fractal-like structure, which may be used to reduce the complexity of the problem. Our previous work done with dimers having orientational dependent activities on planar lattices, 1 XM×N, was possible by considering only one lattice size at a time, M=2,3,4 or 5. The major advantage of the SOM method is to provide a general expression valid for any M and L.
publishDate 1988
normalized_sort_date 1988-07-18T00:00:00Z
dc_date_str 1988-07-18
license_str protected
REPOSITORYNAME FgsRepos
REPOSBASEURL http://hades.library.villanova.edu:8088/fedora
fgs.state Active
fgs.label DIMERS ON TWO- AND THREE-DIMENSIONAL LATTICES: SHIFT OPERATOR MATRIX SOLUTION.
fgs.ownerId diglibEditor
fgs.createdDate 2013-01-22T12:55:46.321Z
fgs.lastModifiedDate 2013-12-05T17:09:24.256Z
dc.title DIMERS ON TWO- AND THREE-DIMENSIONAL LATTICES: SHIFT OPERATOR MATRIX SOLUTION.
dc.creator Phares, Alain J.
Wunderlich, Francis J.
dc.description We use the shift operator matrix (SOM) method developed by McQuistan and Hock to obtain the dimer occupational degeneracies for a three-dimensional L×M×Nlattice. The solution is given in terms of the shift operator, R, which reduces size Nof the lattice by one unit, and the annihilation operators, U, Vand W, of dimers parallel to the L-, M-, and N-axes, respectively. We show that the factorization observed by McQuistan and Hock for monomers distributed on the planar lattice is possible for dimers, and the degeneracy is obtained as a solution of an eigenvalue problem. In particular, it is interesting to note that, as in the monomer case, R- J plays the role of an eigenvalue operator of a matrix which is the Hadamard product of two matrices, one depending on W, and the other on U and V. The matrix depending on W it itself the Kronecker product of order LM of a 2 × 2 matrix. The matrix depending on Uand Vhas an interesting fractal-like structure, which may be used to reduce the complexity of the problem. Our previous work done with dimers having orientational dependent activities on planar lattices, 1 XM×N, was possible by considering only one lattice size at a time, M=2,3,4 or 5. The major advantage of the SOM method is to provide a general expression valid for any M and L.
dc.date 1988-07-18
dc.identifier vudl:179427
dc.source Physics Letter A, Volume 130, number 6, 7, 1988.
dc.language en
license.mdRef http://digital.library.villanova.edu/copyright.html
agent.name Falvey Memorial Library, Villanova University
KHL
has_thumbnail true
THUMBNAIL_contentDigest_type MD5
THUMBNAIL_contentDigest_digest 203c69e18f4f46c81e9892448d2c07cd
THUMBNAIL_contentLocation_type INTERNAL_ID
THUMBNAIL_contentLocation_ref http://hades.library.villanova.edu:8088/fedora/get/vudl:179427/THUMBNAIL/2013-01-22T12:55:48.323Z
relsext.hasModel info:fedora/vudl-system:CoreModel
info:fedora/vudl-system:CollectionModel
info:fedora/vudl-system:ResourceCollection
relsext.itemID oai:digital.library.villanova.edu:vudl:179427
relsext.isMemberOf info:fedora/vudl:179402
relsext.hasLegacyURL http://digital.library.villanova.edu/Villanova%20Digital%20Collection/Faculty%20Fulltext/Wunderlich%20Francis%20J/WunderlichFrancisJ-e53bc960-1d33-4a2c-96e7-7c8e4a842d08.xml
relsext.sortOn title
relsext.sequence vudl:179402#9
_version_ 1504177461510799360
score 13.626031
subpages