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The functional renormalization group (FRG) method calculates probability distributions for sums of correlated random variables. This study computes universal scaling functions for the 3D Ising model, showing accurate agreement with simulations.

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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.