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Universal amplitude ratios for scaling corrections on Ising strips
1Yerevan Physics Institute, Yerevan, Armenia. izmail@yerphi.am
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
This study analyzes finite-size corrections in the Ising model, finding universal amplitude ratios for free energy and correlation length that remain constant across coupling anisotropies. These results are consistent with conformal perturbation theory.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Computational Physics
Background:
- The Ising model is a fundamental model in statistical mechanics.
- Finite-size effects are crucial for understanding phase transitions in realistic systems.
- Boundary conditions significantly influence system behavior.
Purpose of the Study:
- To investigate analytic finite-size corrections in the Ising model on a strip.
- To analyze corrections for free, fixed (++), and mixed boundary conditions.
- To determine the behavior of subdominant corrections to scaling for free energy and inverse correlation length.
Main Methods:
- Exact evaluation of finite-size corrections.
- Analysis of amplitude ratios for varying coupling anisotropy.
- Comparison with conformal perturbation theory.
Main Results:
- Subdominant finite-size corrections follow a specific power-law form: a(p)/N^(2p-1) for free energy and b(p)/N^(2p-1) for inverse correlation length.
- The amplitude ratios b(p)/a(p) are invariant under changes in coupling anisotropy.
- Conformal perturbation theory accurately reproduces these universal behaviors.
Conclusions:
- The Ising model on a strip exhibits universal amplitude ratios for finite-size corrections.
- These universal properties are independent of coupling anisotropy.
- Conformal field theory provides a valid framework for describing these phenomena.
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