Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and General

Spin-1/2lattice systems: a new approach to duality transformations

Héctor Giacomini

Published Jun 21, 1985• 4 citations
Publisher

Abstract

A straightforward algebraic technique is introduced in order to establish duality relations between spin-1/2 lattice systems. A new self-duality relation is found.
DOI
10.1088/0305-4470/18/9/029

Related papers

Duality transformations for spin-1/2lattice systems

Héctor Giacomini

By using a procedure introduced in the previous work, the author considers duality transformations for spin-1/2 lattice systems. The author shows that, in some cases, given a self-dual model, a new self-dual model can be obtained from it. Several examples of this fact are given. In particular the author analyses a system consisting of two interacting Baxter-Wu models, which present close analogies with the Ashkin-Teller model.

Journal of Physics A Mathematical and General•Jun 21, 1985•2 citations

Spin-½ Lattice System: Group Structure and Duality Relation

D. Merlini, C. Gruber

Properties of general lattice systems are investigated using the group properties of such systems. The duality transformation is generalized and is expressed in terms of exact short sequence between the groups associated with one lattice and the groups associated with the dual lattice. A general method is given for constructing explicitly a dual lattice for any lattice system and is illustrated with some two- and three-dimensional models. In particular it is shown that the two-dimensional triangular lattice with three-body forces is self-dual.

Journal of Mathematical Physics•Nov 1, 1972•57 citations

Self-duality conditions for spin systems defined on a new class of non-abelian solvable finite groups

R. Casalbuoni, V. Rittenberg, Shimon Yankielowicz B

Nuclear Physics B•Aug 1, 1980•5 citations

Spin- lattice system: Duality transformation and correlation functions

C. Gruber, D. Merlini, William Greenberg

Physica•Apr 1, 1973•8 citations

Self-duality relation for a three-dimensional spin-1/2lattice system

Héctor Giacomini

A three-dimensional system consisting of a set of interacting two-dimensional Ising models is introduced. It is shown that this model is self-dual. It contains the three-dimensional Ising model as a particular case.

Journal of Physics A Mathematical and General•Jun 21, 1985•1 citation

'Duality twisted' boundary conditions in n-state Potts models

Gunter Markus Schutz

The author discusses a new class of toroidal boundary conditions for one-dimensional quantum Hamiltonians with S n symmetry which are related to two-dimensional n-state Potts models in the extreme anisotropic Hamiltonian limit. At their self-dual point (a point where a second-order phase transition occurs for n=2, 3, 4) the duality transformation is shown to be an additional symmetry giving rise to a new class of 'duality twisted' toroidal boundary conditions. The corresponding Hamiltonians are given in terms of generators of the periodic Temperley-Lieb algebra with an odd number of generators. The author discusses as an example the critical Ising model. Here the complete spectrum for the new boundary conditions can be obtained from a projection mechanism in the spin-1/2 XXZ Heisenberg chain.

Journal of Physics A Mathematical and General•Sep 21, 1993•25 citations
Properties of general lattice systems are investigated using the group properties of such systems. The duality transformation is generalized and is expressed in terms of exact short sequence between the groups associated with one lattice and the groups associated with the dual lattice. A general method is given for constructing explicitly a dual lattice for any lattice system and is illustrated with some two- and three-dimensional models. In particular it is shown that the two-dimensional triangular lattice with three-body forces is self-dual.
The author discusses a new class of toroidal boundary conditions for one-dimensional quantum Hamiltonians with S n symmetry which are related to two-dimensional n-state Potts models in the extreme anisotropic Hamiltonian limit. At their self-dual point (a point where a second-order phase transition occurs for n=2, 3, 4) the duality transformation is shown to be an additional symmetry giving rise to a new class of 'duality twisted' toroidal boundary conditions. The corresponding Hamiltonians are given in terms of generators of the periodic Temperley-Lieb algebra with an odd number of generators. The author discusses as an example the critical Ising model. Here the complete spectrum for the new boundary conditions can be obtained from a projection mechanism in the spin-1/2 XXZ Heisenberg chain.