Finite-size scaling at fixed renormalization-group invariant

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.

Automated summary

Finite-size scaling at fixed renormalization-group invariant is a powerful and flexible technique for analyzing Monte Carlo data at a critical point. By trading statistical fluctuations, significant improvement in statistical accuracy of various quantities can be achieved. Cross-correlations between observables contribute to the large gains in statistical accuracy observed in benchmark tests.