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Exactly solvable interacting spin-ice vertex model.

Anderson A Ferreira1, Francisco C Alcaraz

  • 1Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970, São Carlos, São Paulo, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 16, 2006
PubMed
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We introduce a new solvable five-vertex model on a square lattice with diagonal interactions, generalizing the six-vertex model. Analytical and numerical methods reveal massless phases governed by conformal field theory with c=1.

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Quantum Field Theory

Background:

  • The study of exactly solvable models on lattices is crucial for understanding complex physical phenomena.
  • The six-vertex model is a fundamental model in statistical mechanics, but extensions are needed to capture more intricate interactions.

Purpose of the Study:

  • To introduce and solve a novel family of solvable five-vertex models on a square lattice.
  • To investigate the phase diagram and thermodynamic properties of these models, including their relation to the six-vertex model.
  • To analyze the critical behavior of the observed massless phases.

Main Methods:

  • Development of a special family of five-vertex models incorporating nearest-neighbor and diagonal interactions.
  • Application of the matrix product ansatz for obtaining exact solutions, a technique successful in quantum chains.

Related Experiment Videos

  • Calculation of the phase diagram and free energy in the thermodynamic limit using analytical and numerical analyses.

    • Main Results:

    • The introduced five-vertex models are shown to be exactly solvable.
    • A special limit of these models reproduces the standard six-vertex model.
    • Massless phases were identified, characterized by a conformal field theory with central charge c=1.
    • Continuously varying critical exponents were observed in these massless phases.

    Conclusions:

    • The new five-vertex models offer a valuable extension to exactly solvable lattice models.
    • The findings provide insights into critical phenomena and massless phases in statistical and quantum systems.
    • The study highlights the power of the matrix product ansatz for solving complex interacting systems.