Application of Ewald's Method for Efficient Summation of Dyon Long-Range Potentials

TL;DR

This paper applies Ewald's method, originally from solid state physics, to efficiently compute long-range dyon potentials in SU(2) Yang-Mills theory, reducing finite volume effects in simulations.

Contribution

It introduces the adaptation of Ewald's method for long-range 1/r potentials in dyon models, enabling more accurate finite volume calculations.

Findings

Ewald's method effectively reduces finite volume effects in dyon potential calculations.

The approach can be generalized to other 1/r^p long-range potentials.

Application demonstrated in SU(2) Yang-Mills theory at finite temperature.

Abstract

We study a model of dyons for SU(2) Yang-Mills theory at finite temperature T < T_c, in particular its ability to generate a confining force between a static quark antiquark pair. The interaction between dyons corresponds to a long-range 1/r potential, which in naive treatments with a finite number of dyons typically gives rise to severe finite volume effects. To avoid such effects we apply the so-called Ewald method, which has its origin in solid state physics. The basic idea of Ewald's method is to consider a finite number of dyons inside a finite cubic volume and enforce periodicity of this volume. We explain the technicalities of Ewald's method and outline how the method can be applied to a wider class of 1/r^p long-range potentials.