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Logarithmic conformal field theory and boundary effects in the dimer model
N Sh Izmailian1, V B Priezzhev, Philippe Ruelle
1Institute of Physics, Academia Sinica, Nankang, Taipei, Taiwan.
Physical Review Letters
|February 21, 2006
Summary
Finite-size corrections in the dimer model on a square lattice critically depend on parity. Logarithmic conformal field theory explains this unusual behavior for both free and periodic boundary conditions.
Area of Science:
- Statistical mechanics
- Condensed matter physics
- Quantum field theory
Background:
- The dimer model on a square lattice is a fundamental system in statistical mechanics.
- Understanding finite-size effects is crucial for comparing theoretical models to experimental or numerical results.
- Conformal field theory provides powerful tools for analyzing critical phenomena.
Purpose of the Study:
- To investigate the finite-size corrections of the dimer model on a square lattice.
- To analyze the influence of different boundary conditions (free and periodic) on these corrections.
- To explain the observed finite-size behavior using theoretical frameworks.
Main Methods:
- Analysis of the dimer model on a square lattice.
- Consideration of free and periodic boundary conditions.
- Application of logarithmic conformal field theory.
Main Results:
- Finite-size corrections exhibit a crucial dependence on the parity of the lattice dimensions.
- This parity-dependent behavior is a significant finding for the dimer model.
- The study confirms the applicability of logarithmic conformal field theory to these systems.
Conclusions:
- The finite-size corrections of the dimer model are strongly influenced by lattice parity.
- Logarithmic conformal field theory successfully explains the observed unusual finite-size effects.
- This work provides deeper insights into the critical behavior of lattice models.
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