Determination of the conformal-field-theory central charge by the Wang-Landau algorithm

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• Conformal field theories (CFTs) describe critical phenomena in 2D systems.
• Estimating CFT properties like central charge is crucial for understanding universality classes.
• Traditional methods for calculating central charge can be computationally intensive.

Purpose of the Study:

• To present a simple and precise method for estimating the central charge of 2D lattice models at critical points.
• To apply the Wang-Landau flat-histogram algorithm for free energy calculations.
• To validate the method on various lattice models and discuss conformal weights.

Main Methods:

• Utilizing Monte Carlo simulations with the Wang-Landau flat-histogram algorithm.
• Calculating the free energy of lattice models on a torus as a function of torus radii.
• Analyzing the free-energy scaling at the critical point to determine the central charge.

Main Results:

• The method provides a precise estimation of the central charge for 2D lattice models.
• Successful application to Ising, tricritical Ising (Blume-Capel), Potts, and site-diluted Ising models.
• Demonstrated the capability to estimate conformal weights.

Conclusions:

• The presented method offers an efficient and accurate approach to determine central charges from simulations.
• This technique enhances the study of critical phenomena and conformal field theories in condensed matter systems.
• The approach is versatile and applicable to a range of 2D lattice models.