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Confinement viewed with dimeron and dyon ensembles
(Humboldt Univ. Berlin)
Aula Seminari (LNF)
Via Enrico Fermi, 40
00044 Frascati (Roma)
We describe two recent attempts to simulate dimeron and dyon ensembles.
For zero temperature following old confinement ideas put forward by Callan, Dashen and Gross (anti-) dimeron configurations are Monte-Carlo sampled according to their classical action. We show that with an increasing bare coupling the dimerons become more and more dissociating pointing to a meron picture of the QCD vacuum state. Confinement is then viewed numerically in terms of an area law of Wilson loops or an approximate linearly rising potential.
For non-zero temperature guided by caloron solutions with non-trivial holonomy as invented by Kraan and van Baal a couple of years ago we discuss ensembles of (anti-) dyon caloron constituents. Approximating them as Abelian monopoles one analytically can compute the string tension as a function of the dyon gas density and the temperature.
On the other hand simulating the monopole gas numerically one easily sees that the long-range tails of their respective fields cannot be simply treated within a finite volume. We describe that a solution of the severe finite-size problem can be found with Ewald's summation technique well-known in plasma physics. The numerical result obtained in the infinite volume limit nicely agrees with the analytical result.