arXiv:1509.06324 · Journal of Physics A Mathematical and Theoretical

Influence of boundary conditions on bulk properties of six-vertex model

Thiago Silva Tavares, G A P Ribeiro, V. E. Korepin

Published Oct 20, 2015• 12 citations

Abstract

We study the influence of boundary conditions on the entropy of the six-vertex model. We consider the case of fixed boundary conditions in order to argue that the entropy of the six-vertex model vary continuously from its value for ferroelectric to periodic boundary conditions. This is done by merging the ferroelectric boundary and the Néel boundary.

DOI: 10.1088/1751-8113/48/45/454004

Related papers

The entropy of the six-vertex model with a variety of different boundary conditions

T S Tavares, G A P Ribeiro, V. E. Korepin

We study the dependence of entropy [per lattice site] of six-vertex model on boundary conditions. We start with lattices of finite size and then proceed to thermodynamic limit. We argue that the six-vertex model with periodic, anti-periodic and mixed boundary conditions produce the same free-energy in the thermodynamic limit. We have found fixed boundary conditions such that the entropy varies continuously from zero to its value for periodic boundary condition. We have also shown that the physical quantities of the six-vertex model at the isotropic point does not change in the case of singular toroidal boundary.

arXiv:1501.02818Journal of Statistical Mechanics Theory and ExperimentJun 10, 201511 citations

The Influence of Boundary Conditions in the Six-Vertex Model

Paul Zinn-Justin

We discuss the influence of boundary conditions on the continuum limit of the six-vertex model by deriving a variational principle for the associated height function with arbitrary fixed boundary conditions. We discuss its consequences using the known phase diagram of the six-vertex model. In some particular cases we compute explicitly the corresponding partial differential equations by means of the Bethe Ansatz.

arXiv:cond-mat/0205192May 9, 200227 citations

The arctic curve of the domain-wall six-vertex model in its anti-ferroelectric regime

Colomo, F., Pronko, A. G., Paul Zinn-Justin

An explicit expression for the spatial curve separating the region of ferroelectric order (`frozen' zone) from the disordered one (`temperate' zone) in the six-vertex model with domain wall boundary conditions in its anti-ferroelectric regime is obtained.

Jan 1, 201034 citations

The arctic curve of the domain wall six-vertex model in its antiferroelectric regime

F Colomo, A G Pronko, Paul Zinn-Justin

An explicit expression for the spatial curve separating the region of ferroelectric order ('frozen' zone) from the disordered one ('temperate' zone) in the six-vertex model with domain wall boundary conditions in its antiferroelectric regime is obtained.

arXiv:1001.2189Journal of Statistical Mechanics Theory and ExperimentMar 4, 201038 citations

Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions

Murray T. Batchelor, R. J. Baxter, M J O'Rourke +1 more

We consider the six-vertex model with anti-periodic boundary conditions across a finite strip. The row-to-row transfer matrix is diagonalized by the 'commuting transfer matrices' method. From the exact solution we obtain an independent derivation of the interfacial tension of the six-vertex model in the anti-ferroelectric phase. The nature of the corresponding integrable boundary condition on the XXZ spin chain is also discussed.

arXiv:hep-th/9502040Journal of Physics A Mathematical and GeneralMay 21, 199598 citations

The 6-Vertex Model with Fixed Boundary Conditions

Nicolai Reshetikhin

We study the 6-vertex model with fixed boundary conditions.In the thermodynamical limit there is a formation of the limit shape.We collect most of the known results about the analytical properties of the free energy of the model as the function of electric fields and study the asymptotical behavior near singularities.We also study the asymptotic of limit shapes and the structure of correlation functions in the bulk Bethe Ansatz: 75 years later October 19-21 2006, Brussels,

Aug 8, 200717 citations