Bayesian inference in the scaling analysis of critical phenomena

Area of Science:

• Statistical physics
• Computational physics
• Bayesian inference

Background:

• Critical phenomena exhibit universal behaviors independent of microscopic details.
• Finite-size scaling analysis is crucial for understanding critical points.
• Traditional methods like least-squares regression have limitations with complex data.

Purpose of the Study:

• To develop a novel statistical inference method for scaling analysis of critical phenomena.
• To test the universality class of critical phenomena using this new method.
• To overcome limitations of existing methods in analyzing complex scaling data.

Main Methods:

• Utilizing Bayesian statistics, specifically Gaussian process regression.
• Assuming only the smoothness of a scaling function, without requiring a predefined form.
• Applying the method to finite-size scaling analysis of Ising models on square and triangular lattices.

Main Results:

• The proposed method demonstrates accuracy comparable to least-squares near the critical point.
• It successfully analyzes data unsuitable for low-degree polynomial least-squares regression.
• Universality of the 2D Ising model's finite-size scaling function is confirmed by comparing lattice data.

Conclusions:

• The Gaussian process regression method provides a robust tool for critical phenomena analysis.
• This approach validates the universality of the 2D Ising model's scaling functions.
• The method offers a powerful alternative for analyzing complex scaling data in statistical physics.