Controlling One-Dimensional Langevin Dynamics on the Lattice

Details Controlling One-Dimensional Langevin Dynamics on the Lattice Controlling One-Dimensional Langevin Dynamics on the Lattice

1999-03-03

arxiv.org/abs/hep-lat/9903007v1

Phys.Rev. D60 (1999) 105039

Physics

High Energy Physics

High Energy Physics - Lattice

10 pages, 5 figures, uses RevTex

Scientific paper

10.1103/PhysRevD.60.105039

Stochastic evolutions of classical field theories have recently become popular in the study of problems such as determination of the rates of topological transitions and the statistical mechanics of nonlinear coherent structures. To obtain high precision results from numerical calculations, a careful accounting of spacetime discreteness effects is essential, as well as the development of schemes to systematically improve convergence to the continuum. With a kink-bearing $\phi^4$ field theory as the application arena, we present such an analysis for a 1+1-dimensional Langevin system. Analytical predictions and results from high resolution numerical solutions are found to be in excellent agreement.

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