Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 11, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP11(2012)140
Keywords
Lattice Quantum Field Theory; Sigma Models
Categories
Funding
- Schweizerischer Nationalfonds (SNF)
- Innovations- und Kooperationsprojekt C-13 of the Schweizerische Universitatskonferenz (SUK/CRUS)
- Hungarian National Science Fund OTKA [K 777100]
- Regione Lombardia
- CILEA Consortium through a LISA grant
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We investigate the cutoff effects in 2-d lattice O(N) models for a variety of lattice actions, and we identify a class of very simple actions for which the lattice artifacts are extremely small. One action agrees with the standard action, except that it constrains neighboring spins to a maximal relative angle delta. We fix delta by demanding that a particular value of the step scaling function agrees with its continuum result already on a rather coarse lattice. Remarkably, the cutoff effects of the entire step scaling function are then reduced to the per mine level. This also applies to the theta-vacuum effects of the step scaling function in the 2-d O(3) model. The cutoff effects of other physical observables including the renormalized coupling g(R) and the mass in the isotensor channel are also reduced drastically. Another choice, the mixed action, which combines the standard quadratic with an appropriately tuned large quartic term, also has extremely small cutoff. effects. The size of cutoff effects is also investigated analytically in 1-d and at N = infinity in 2-d.
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