Critical Probability Distributions of the Order Parameter from the Functional Renormalization Group

Area of Science:

• Statistical Physics
• Quantum Field Theory
• Computational Physics

Background:

• Calculating probability distribution functions (PDFs) for sums of strongly correlated random variables is challenging.
• The Ising model is a fundamental model in statistical physics, often studied at criticality.

Purpose of the Study:

• To demonstrate the capability of the functional renormalization group (FRG) for computing PDFs of correlated random variables.
• To calculate universal scaling functions for the 3D Ising model at criticality.

Main Methods:

• Application of the functional renormalization group (FRG) method.
• Utilizing the simplest implementation of FRG.
• Focusing on the three-dimensional Ising model at its critical point.

Main Results:

• Successful computation of the probability distribution functions for the order parameter and its logarithm (rate functions).
• Determination of the complete family of universal scaling functions in the thermodynamic limit.
• Accurate comparison of FRG results with numerical simulations.

Conclusions:

• The FRG provides a powerful tool for calculating PDFs in strongly correlated systems.
• The computed scaling functions for the 3D Ising model are universal and validated by simulations.