Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Boundary polarization in the six-vertex model.

N M Bogoliubov1, A V Kitaev, M B Zvonarev

  • 1Steklov Institute of Mathematics at St. Petersburg, Fontanka 27, St. Petersburg 191011, Russia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
PubMed
Summary

Boundary effects in the six-vertex model persist even at large scales. Domain wall boundary conditions influence macroscopic quantities, impacting predictions from conformal field theory.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Dynamical properties of the one-dimensional spin-1/2 Bose-Hubbard model near a Mott-insulator to ferromagnetic-liquid transition.

Physical review letters·2009
Same author

Thermodynamics of the spin Luttinger liquid in a model ladder material.

Physical review letters·2008
Same author

Spin dynamics in a one-dimensional ferromagnetic bose gas.

Physical review letters·2008
Same author

Directed-loop Monte Carlo simulations of vertex models.

Physical review. E, Statistical, nonlinear, and soft matter physics·2004
Same author

Nonunitary spin-charge separation in a one-dimensional fermion gas.

Physical review letters·2004
Same author

Quantum dynamics of strongly interacting boson systems: atomic beam splitters and coupled Bose-Einstein condensates.

Physical review letters·2001

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • The six-vertex model is a fundamental model in statistical mechanics.
  • Domain wall boundary conditions introduce specific constraints at the lattice edges.

Purpose of the Study:

  • To analyze vertical-arrow fluctuations near boundaries in the six-vertex model.
  • To understand the impact of boundary conditions on macroscopic properties in the large N limit.

Main Methods:

  • Expressing the one-point correlation function (boundary polarization) using the partition function on a sublattice.
  • Representing the partition function using orthogonal polynomials.
  • Analyzing the large N limit of the model.

Main Results:

  • The boundary polarization is directly related to the partition function of a sublattice.

Related Experiment Videos

  • The presence of boundaries affects macroscopic quantities even as the lattice size (N) becomes large.
  • Logarithmic terms arising from boundary effects were identified.

    • Conclusions:

    • Boundary effects in the six-vertex model are significant and do not vanish in the large N limit.
    • The study provides a connection between orthogonal polynomials, partition functions, and boundary phenomena.
    • Results offer insights for comparing with conformal field theory predictions.