Calculation of the shift exponent for the two-layer three-state Potts model using the transfer matrix method

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics

Background:

• The behavior of magnetic and other systems near phase transitions is often described by critical exponents.
• Potts models are widely used to study phase transitions in various physical systems.
• Understanding the critical properties of multi-layer systems is crucial for developing new materials and devices.

Purpose of the Study:

• To calculate the critical temperature and critical exponent for symmetric and asymmetric two-layer three-state Potts models.
• To investigate the validity of scaling arguments for the shift exponent (phi) in these models.
• To compare theoretical predictions with numerical results for different intralayer interaction scenarios.

Main Methods:

• A finite-size scaling approach was employed.
• The transfer matrix method was utilized for calculations.
• The study focused on two-layer three-state Potts models with varying intralayer interactions.

Main Results:

• For similar intralayer interactions, the calculated shift exponent (phi) confirmed predictions (phi = gamma, where gamma is the susceptibility exponent).
• For unequal intralayer interactions, a shift exponent of phi = 0.5 was obtained.
• This result for unequal interactions deviates from the prediction of a generalized mean-field theory (phi = gamma/2).

Conclusions:

• The finite-size scaling approach provides accurate critical exponents for multi-layer Potts models.
• Scaling arguments are validated for symmetric systems, highlighting the importance of intralayer interactions.
• The discrepancy for asymmetric systems suggests limitations of generalized mean-field theories in describing complex multi-layer interactions.