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Quantifying nonuniversal corner free-energy contributions in weakly anisotropic two-dimensional critical systems
Florian Kischel1, Stefan Wessel1
1Institute for Theoretical Solid State Physics, <a href="https://ror.org/04xfq0f34">RWTH Aachen University</a>, Otto-Blumenthal Straße 26, 52074 Aachen, Germany.
Physical Review. E
|September 19, 2024
Summary
Researchers developed a formula for corner free-energy in 2D critical systems. This work quantifies nonuniversality and applies to Ising and Potts models, aiding critical phenomena studies.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Critical Phenomena
Background:
- Corner free-energy contributions are crucial for understanding critical phenomena in 2D systems.
- Anisotropy introduces complexities in universal behavior, particularly at critical points.
- Conformal Field Theory (CFT) provides a framework for describing critical 2D systems in their isotropic limit.
Purpose of the Study:
- To derive an exact formula for the corner free-energy contribution in weakly anisotropic 2D critical systems.
- To investigate the nonuniversality of corner terms in anisotropic systems.
- To establish the applicability of the derived formula to various critical models.
Main Methods:
- Derivation of an exact analytical formula for corner free-energy.
- Numerical exact calculations for the anisotropic triangular Ising model.
- Application of the formula to three-states and four-states Potts models.
Main Results:
- An exact formula for corner free-energy in weakly anisotropic 2D Ising-class systems was derived.
- The formula quantifies the nonuniversality of the corner term for anisotropic systems.
- Agreement was found between the derived formula and numerical calculations for the anisotropic triangular Ising model.
Conclusions:
- The derived formula provides a general method for calculating corner free-energy in anisotropic 2D critical systems.
- The findings highlight the nonuniversal nature of corner contributions in anisotropic systems.
- The formula is expected to be applicable to other anisotropic 2D critical systems describable by CFT in the isotropic limit.
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