Universality, Lee-Yang Singularities, and Series Expansions

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Condensed Matter Physics

Background:

• Reconstructing the equation of state near critical points is crucial for understanding phase transitions.
• Existing methods often require extensive data or are limited in applicability.
• Taylor coefficients provide a finite, computable representation of system behavior away from singularities.

Purpose of the Study:

• To develop a novel method for reconstructing the equation of state near a second-order critical point.
• To efficiently extract critical point information from Taylor coefficients computed away from the critical point.
• To demonstrate the method's applicability to the Ising universality class and the Gross-Neveu model.

Main Methods:

• Utilizing a finite set of Taylor coefficients.
• Employing Padé resummation techniques.
• Applying conformal mapping for singularity analysis.

Main Results:

• Successfully reconstructed the equation of state near critical points.
• Efficiently extracted the Lee-Yang edge singularity, pinpointing the critical point location.
• Constrained nonuniversal parameters for mapping to the Ising model in the scaling regime.
• Numerically evaluated the equation of state in the critical vicinity.

Conclusions:

• The proposed method offers an efficient way to determine critical point properties from off-critical data.
• This technique is broadly applicable to systems within the Ising universality class.
• The study validates the method using the Gross-Neveu model, showcasing its practical utility.