High Precision Fourier Monte Carlo Simulation of Crystalline Membranes

TL;DR

This paper introduces an improved Fourier Monte Carlo algorithm that significantly reduces critical slowing down, enabling highly accurate simulations of crystalline membranes and providing new estimates for critical exponents.

Contribution

The authors develop a modified Fourier Monte Carlo method with wave vector-specific acceptance rates, enhancing efficiency and accuracy in simulating lattice models with long-range interactions.

Findings

Achieved a precise estimate of the critical exponent eta as 0.795(10).

Demonstrated the importance of accounting for corrections to scaling in finite size analyses.

Showed that the improved algorithm allows simulation of larger systems, clarifying previous discrepancies.

Abstract

We report an essential improvement of the plain Fourier Monte Carlo algorithm that promises to be a powerful tool for investigating critical behavior in a large class of lattice models, in particular those containing microscopic or effective long-ranged interactions. On tuning the Monte Carlo acceptance rates separately for each wave vector, we are able to drastically reduce critical slowing down. We illustrate the resulting efficiency and unprecedented accuracy of our algorithm with a calculation of the universal elastic properties of crystalline membranes in the flat phase and derive a numerical estimate eta = 0.795(10) for the critical exponent eta that challenges those derived from other recent simulations. The large system sizes accessible to our present algorithm also allow to demonstrate that insufficiently taking into account corrections to scaling may severely hamper a finite size scaling analysis. This observation may also help to clarify the apparent disagreement of published numerical estimates of eta in the existing literature.