Yang-Lee zeros of certain antiferromagnetic models

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Phase Transitions

Background:

• Yang-Lee zeros are crucial for understanding phase transitions in magnetic systems.
• The Ising antiferromagnet, particularly its Yang-Lee zeros, remains less explored.
• Investigating these zeros provides insights into critical phenomena and complex phase boundaries.

Purpose of the Study:

• To analyze the Yang-Lee zeros of the Ising antiferromagnet using nearest-neighbor and mean-field models.
• To characterize the high-temperature behavior and scaling of these zeros.
• To identify and illustrate phase transitions and complex phase boundaries through root curve analysis.

Main Methods:

• Studied nearest-neighbor and mean-field Ising models.
• Derived high-temperature expansions for Yang-Lee zeros in terms of inverse temperature.
• Computed partition functions and analyzed mean-field polynomials numerically and analytically.
• Identified root curves for ferromagnetic and antiferromagnetic cases.

Main Results:

• Logarithm of Yang-Lee zeros expands in half odd integer powers of inverse temperature (∼k^{1/2}) in the high-temperature limit.
• Identities for expansion coefficients were found and numerically verified for the nearest-neighbor model.
• Mean-field polynomials for ferromagnetic and antiferromagnetic cases were analyzed, revealing new root curves.
• Root curves clearly illustrate phase transitions and complex phase boundaries, including regions of complex staggered magnetization.

Conclusions:

• The high-temperature behavior of Yang-Lee zeros exhibits universal scaling (∼k^{1/2}) across dimensions and lattices.
• Mean-field models provide a tractable framework to study complex phase boundaries and transitions via root curves.
• The identified root curves offer a novel perspective on phase transitions in Ising models, particularly for the antiferromagnetic case.