Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1999-11-11
Int.J.Mod.Phys.A15:3341-3368,2000
Physics
High Energy Physics
High Energy Physics - Lattice
26 pages, 11 figures
Scientific paper
10.1142/S0217751X00001097
We perform renormalization group transformations to construct optimally local perfect lattice actions for free scalar fields of any mass. Their couplings decay exponentially. The spectrum is identical to the continuum spectrum, while thermodynamic quantities have tiny lattice artifacts. To make such actions applicable in simulations, we truncate the couplings to a unit hypercube and observe that spectrum and thermodynamics are still drastically improved compared to the standard lattice action. We show how preconditioning techniques can be applied successfully to this type of action. We also consider a number of variants of the perfect lattice action, such as the use of an anisotropic or triangular lattice, and modifications of the renormalization group transformations motivated by wavelets. Along the way we illuminate the consistent treatment of gauge fields, and we find a new fermionic fixed point action with attractive properties.
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