Locating Critical Points Using Ratios of Lee-Yang Zeros

Area of Science:

• Statistical Physics
• Computational Physics
• Phase Transitions

Background:

• Locating critical points is crucial for understanding phase transitions in various physical systems.
• Traditional methods like Binder-cumulant analysis can be affected by finite-volume effects, especially in complex systems.
• Lee-Yang zeros offer a theoretical framework for analyzing critical phenomena.

Purpose of the Study:

• To introduce a novel numerical method for precisely determining critical points in general systems.
• To leverage the finite-size scaling of Lee-Yang zeros for enhanced accuracy.
• To demonstrate the method's advantage over existing techniques in mitigating finite-volume effects.

Main Methods:

• Utilizing the finite-size scaling properties of Lee-Yang zeros.
• Analyzing the intersection of Lee-Yang zero ratios across different spatial volumes.
• Applying the method to the three-dimensional three-state Potts model with a non-zero external field.

Main Results:

• The proposed method successfully identifies the critical point.
• Demonstrated suppression of finite-volume effects, particularly in systems with mixed variables.
• Validation through application to a complex model system (3D 3-state Potts model).

Conclusions:

• The finite-size scaling of Lee-Yang zeros provides a robust numerical tool for critical point determination.
• This method offers superior accuracy by minimizing finite-volume artifacts compared to conventional approaches.
• The technique is effective even in complex systems like the Potts model with external fields.