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arXiv · 2112.00392

Finite-Size Scaling at fixed Renormalization-Group invariant

Francesco Parisen Toldin
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Abstract

Finite-size scaling at fixed renormalization-group invariant is a powerful and flexible technique to analyze Monte Carlo data at a critical point. It consists in fixing a given renormalization-group invariant quantity to a given value, thereby trading its statistical fluctuations with those of a parameter driving the transition. One remarkable feature is the observed significant improvement of statistical accuracy of various quantities, as compared to a standard analysis. We review the method, discussing in detail its implementation, the error analysis, and a previously introduced covariance-based optimization. Comprehensive benchmarks on the Ising model in two and three dimensions show large gains in the statistical accuracy, which are due to cross-correlations between observables. As an application, we compute an accurate estimate of the inverse critical temperature of the improved O(2) $\phi^4$ model on a three-dimensional cubic lattice.

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BibTeXRIS

Francesco Parisen Toldin. 2021-12-01. Finite-Size Scaling at fixed Renormalization-Group invariant. https://doi.org/10.1103/physreve.105.034137

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