Finite-size scaling at fixed renormalization-group invariant

Area of Science:

• Statistical Physics
• Computational Physics
• Critical Phenomena

Background:

• Finite-size scaling is crucial for analyzing critical phenomena in statistical physics.
• Standard analysis methods can be limited by statistical fluctuations near critical points.

Purpose of the Study:

• To review and detail the finite-size scaling technique at fixed renormalization-group invariant.
• To demonstrate its effectiveness in improving statistical accuracy for Monte Carlo data.
• To apply the method for calculating critical temperature in a complex model.

Main Methods:

• Implementing finite-size scaling by fixing a renormalization-group invariant quantity.
• Analyzing statistical fluctuations and employing covariance-based optimization.
• Benchmarking the method on the 2D and 3D Ising models.

Main Results:

• Significant improvements in statistical accuracy for various observables were observed.
• Cross-correlations between observables were identified as the source of accuracy gains.
• Accurate estimation of the inverse critical temperature for the improved O(2) phi^4 model was achieved.

Conclusions:

• Finite-size scaling at fixed renormalization-group invariant is a powerful and flexible technique.
• The method offers substantial improvements in statistical accuracy compared to standard approaches.
• This technique provides a robust framework for critical phenomena research.