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

arXiv:cond-mat/9610184 · Physical Review Letters

Exact Solution of a Three-Dimensional Dimer System

H. Y. Huang, Vladislav Popkov, Fa Yueh Wu

Published Jan 20, 1997• 13 citations
arXivHTMLPDF

Abstract

We present the exact solution of a three-dimensional lattice-statistical model consisting of layers of vertex models coupled with interlayer interactions. For a particular nontrivial interlayer interaction between charge-conserving vertex models and using a transfer matrix approach, we show that the eigenvalues and eigenvectors of the transfer matrix are related to those of the two-dimensional vertex model. As an illustration of the general solution, we analyze the phase transitions in a realistic three-dimensional dimer system and determine its phase diagram and nature of transitions.

DOI
10.1103/physrevlett.78.409

Related papers

Lattice statistics in three dimensions: Solution of layered dimer and layered domain wall models

Vladislav Popkov, Doochul Kim, H. Y. Huang +1 more

Analyses are given for two three-dimensional lattice systems: A system of close-packed dimers placed in layers of honeycomb lattices and a layered triangular-lattice interacting domain wall model, both with nontrivial interlayer interactions. We show that both models are equivalent to a five-vertex model on the square lattice with interlayer vertex-vertex interactions. Using the method of Bethe ansatz, a closed-form expression for the free energy is obtained and analyzed. We deduce the exact phase diagram and determine the nature of the phase transitions determined as a function of the strength of the interlayer interaction.

arXiv:cond-mat/9703065•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Oct 1, 1997•4 citations

3-Dimensional Multilayered 6-vertex Statistical Model: Exact Solution

Vladislav Popkov, Bernard Nienhuis

Solvable via Bethe Ansatz (BA) anisotropic statistical model on cubic lattice consisting of locally interacting 6-vertex planes, is studied. Symmetries of BA lead to infinite hierarchy of possible phases, which is further restricted by numerical simulations. The model is solved for arbitrary value of the interlayer coupling constant. Resulting is the phase diagram in general 3-parameter space. Exact mapping onto the models with some inhomogenious sets of interlayer coupling constants is established.

arXiv:cond-mat/9611117•Nov 14, 1996•0 citations

The 3D multi-layered solvable six-vertex model: The phase diagram

Vladislav Popkov, Bernard Nienhuis

An anisotropic statistical model on a cubic lattice consisting of locally interacting six-vertex planes solvable via Bethe ansatz (BA), is studied. Symmetries of BA lead to an infinite hierarchy of possible phases, which is further restricted by numerical simulations. The model is solved for an arbitrary value of the interlayer coupling constant. Resulting is the phase diagram in general three-parameter space. Two new phases of chiral (spiral) character and a new first-order phase transition appear due to the interplane interaction. Exact mapping onto the models with some inhomogeneous sets of interlayer coupling constants is established.

Journal of Physics A Mathematical and General•Jan 7, 1997•3 citations

FERMIONIC STRINGS AND THE EXACT SOLUTION OF EDGE MODELS IN THREE DIMENSIONS

Peter Orland A. B. C

A three-dimensional statistical system, called here the six-edge model, is shown, for a particular domain of parameters, to be equivalent to a theory of Fermionic strings. This model has a local U(1) gauge invariance, similiar to the global invariance of the two-dimensional six-vertex model. Further restricting the parameters gives a system named here the five-edge model, which is exactly solvable. The conformal anomaly of the surfaces is calculated. The transfer matrix is diagonalized, and the free energy, phase diagram and correlation length are determined exactly. The surfaces of the model display a roughening transition similiar to that analyzed by Blöte, Hilhorst and Nienhuis.

International Journal of Modern Physics B•Aug 20, 1991•7 citations

Interacting dimers on the honeycomb lattice: an exact solution of the five-vertex model

H. Y. Huang, Fa Yueh Wu, Kunz, H. +1 more

The problem of close-packed dimers on the honeycomb lattice was solved by Kasteleyn in 1963. Here we extend the solution to include interactions between neighboring dimers in two spatial lattice directions. The solution is obtained by using the method of Bethe ansatz and by converting the dimer problem into a five-vertex problem. The complete phase diagram is obtained and it is found that a new frozen phase, in which the attracting dimers prevail, arises when the interaction is attractive. For repulsive dimer interactions a new first-order line separating two frozen phases occurs. The transitions are continuous and the critical behavior in the disorder regime is found to be the same as in the case of noninteracting dimers characterized by a specific heat exponent α = 12.

•Jan 1, 1996•18 citations

Exact solution of a vertex model with unlimited number of states per bond

F C Alcaraz, R Z Bariev

The exact solution is obtained for the eigenvalues and eigenvectors of the row-to-row transfer matrix of a two-dimensional vertex model with an unlimited number of states per bond. This model is a classical counterpart of a quantum spin chain with an unlimited value of spin. This quantum chain is studied using general predictions of conformal field theory. The long-distance behaviour of some ground state correlation functions is derived from a finite-size analysis of the gapless excitations.

arXiv:cond-mat/9904040•Journal of Physics A Mathematical and General•Jan 1, 1999•2 citations
We present the exact solution of a three-dimensional lattice-statistical model consisting of layers of vertex models coupled with interlayer interactions. For a particular nontrivial interlayer interaction between charge-conserving vertex models and using a transfer matrix approach, we show that the eigenvalues and eigenvectors of the transfer matrix are related to those of the two-dimensional vertex model. As an illustration of the general solution, we analyze the phase transitions in a realistic three-dimensional dimer system and determine its phase diagram and nature of transitions.
Analyses are given for two three-dimensional lattice systems: A system of close-packed dimers placed in layers of honeycomb lattices and a layered triangular-lattice interacting domain wall model, both with nontrivial interlayer interactions. We show that both models are equivalent to a five-vertex model on the square lattice with interlayer vertex-vertex interactions. Using the method of Bethe ansatz, a closed-form expression for the free energy is obtained and analyzed. We deduce the exact phase diagram and determine the nature of the phase transitions determined as a function of the strength of the interlayer interaction.
Solvable via Bethe Ansatz (BA) anisotropic statistical model on cubic lattice consisting of locally interacting 6-vertex planes, is studied. Symmetries of BA lead to infinite hierarchy of possible phases, which is further restricted by numerical simulations. The model is solved for arbitrary value of the interlayer coupling constant. Resulting is the phase diagram in general 3-parameter space. Exact mapping onto the models with some inhomogenious sets of interlayer coupling constants is established.
An anisotropic statistical model on a cubic lattice consisting of locally interacting six-vertex planes solvable via Bethe ansatz (BA), is studied. Symmetries of BA lead to an infinite hierarchy of possible phases, which is further restricted by numerical simulations. The model is solved for an arbitrary value of the interlayer coupling constant. Resulting is the phase diagram in general three-parameter space. Two new phases of chiral (spiral) character and a new first-order phase transition appear due to the interplane interaction. Exact mapping onto the models with some inhomogeneous sets of interlayer coupling constants is established.
A three-dimensional statistical system, called here the six-edge model, is shown, for a particular domain of parameters, to be equivalent to a theory of Fermionic strings. This model has a local U(1) gauge invariance, similiar to the global invariance of the two-dimensional six-vertex model. Further restricting the parameters gives a system named here the five-edge model, which is exactly solvable. The conformal anomaly of the surfaces is calculated. The transfer matrix is diagonalized, and the free energy, phase diagram and correlation length are determined exactly. The surfaces of the model display a roughening transition similiar to that analyzed by Blöte, Hilhorst and Nienhuis.
The problem of close-packed dimers on the honeycomb lattice was solved by Kasteleyn in 1963. Here we extend the solution to include interactions between neighboring dimers in two spatial lattice directions. The solution is obtained by using the method of Bethe ansatz and by converting the dimer problem into a five-vertex problem. The complete phase diagram is obtained and it is found that a new frozen phase, in which the attracting dimers prevail, arises when the interaction is attractive. For repulsive dimer interactions a new first-order line separating two frozen phases occurs. The transitions are continuous and the critical behavior in the disorder regime is found to be the same as in the case of noninteracting dimers characterized by a specific heat exponent α = 12.