Phase transition in the 2D random Potts model in the large-q limit

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• The two-dimensional q-state Potts model is a fundamental model in statistical mechanics.
• Understanding phase transitions in disordered systems is crucial for condensed matter physics.

Purpose of the Study:

• To investigate the phase transition in the 2D q-state Potts model with random ferromagnetic couplings in the large-q limit.
• To determine the critical behavior and exponents of this disordered system.

Main Methods:

• Utilized a combinatorial optimization algorithm.
• Employed approximate mappings to analyze the model.
• Focused on the large-q limit for theoretical tractability.

Main Results:

• Conjectured critical behavior is controlled by the infinite randomness fixed point of the random transverse-field Ising spin chain.
• Derived exact critical exponents: beta=(3-sqrt[5])/4, beta(s)=1/2, and nu=1.
• Observed logarithmic singularity in specific heat with strong sample-to-sample fluctuations at the transition.
• Found discontinuities in internal energy due to discretized randomness.

Conclusions:

• The study provides insights into the critical phenomena of disordered magnetic systems.
• The findings connect the Potts model to the Ising spin chain universality class.
• The exact critical exponents offer valuable benchmarks for theoretical and numerical studies.