Beating Monte Carlo: The Polynomial Method in Lattice Problems

Executive Summary

In order to address long-standing questions in the study of phase transitions, we will extend a newly developed method for performing calculations for lattice models. While early versions of this method have significantly outperformed the Monte Carlo method in two-dimensional calculations, a new version extended to three dimensions could be applied to critical calculations in lattice quantum chromodynamics in support of national missions and would be a monumental achievement in the field of physics.

Publications, Presentations, and Patents

C. R. Scullard and J. L. Jacobsen. 2020. "Bond percolation thresholds on Archimedean lattices from critical polynomial roots,: Phys. Rev. Research 2, 012050.

C. R. Scullard, J. L. Jacobsen and R. M. Ziff. 2021. "Critical percolation on the kagome hypergraph," J. Phys. A: Math. Theor. 54, 055006.