Finite-Size Scaling at fixed Renormalization-Group invariant

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) ${\varphi }^4$ model on a three-dimensional cubic lattice.

12 pages, 2 figures; v2: 12 pages, 2 figures, new MC simulations at L=384, revised critical beta of the improved XY model; v3: 12 pages, 2 figures, expanded introduction and summary

References in corpus (12)

• The critical exponents of the superfluid transition in He4
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Monte Carlo study of an improved clock model in three dimensions
• Monte Carlo study of a generalized icosahedral model on the simple cubic lattice
• Aspect-ratio dependence of thermodynamic Casimir forces
• Universal dependence on disorder of 2D randomly diluted and random-bond +-J Ising models
• The 3D +-J Ising model at the ferromagnetic transition line
• Precision check on triviality of phi^4 theory by a new simulation method
• Critical Casimir forces and adsorption profiles in the presence of a chemically structured substrate
• Cross-correlations in scaling analyses of phase transitions
• Finite-size effects in canonical and grand-canonical quantum Monte Carlo simulations for fermions
• Mean-value identities as an opportunity for Monte Carlo error reduction

Cited by in corpus (4)

• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• The ordinary surface universality class of the three-dimensional O($N$) model
• Universal finite-size scaling in the extraordinary-log boundary phase of three-dimensional $O(N)$ model
• ${\varphi }^4$ lattice model with cubic symmetry in three dimensions: RG-flow and first order phase transitions