Lattice Realization of Complex Conformal Field Theories: Two-Dimensional Potts Model with Q>4 States

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Quantum Field Theory

Background:

• The two-dimensional Q-state Potts model with real couplings is known to exhibit a first-order phase transition for Q>4.
• Understanding the behavior of such models at and beyond this transition is crucial for theoretical physics.

Purpose of the Study:

• To investigate a loop-model realization of the Q-state Potts model where Q is treated as a continuous parameter.
• To explore the emergence of complex conformal theories and the analytic continuation of critical exponents for Q>4.

Main Methods:

• Utilizing a loop-model framework that allows Q to be a continuous variable.
• Employing transfer-matrix computations to verify theoretical predictions for specific cases like Q=5.

Main Results:

• The study reveals a collision of critical and tricritical fixed points at Q=4.
• For Q>4, these points emerge as complex conformally invariant theories, even with complex coupling constants.
• All critical exponents can be derived through analytic continuation from known results for Q≤4.

Conclusions:

• The continuous loop model provides a powerful framework for studying the Q-state Potts model beyond its traditional parameter range.
• Complex conformal theories arise naturally for Q>4, offering new insights into critical phenomena.
• Analytic continuation of critical exponents is a valid approach for understanding these complex systems.