Scaling in a toy model of gluodynamics at finite temperatures

1998/03/24 by В. К. Петров, V. K. Petrov, Petrov, V. K.
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Geometry #Lattice (music) #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum Chromodynamics and Particle Interactions #Scaling #Scaling limit #String (physics) #Theoretical and Computational Physics #hep-lat

paper · pdf · doi:10.48550/arxiv.hep-lat/9803019

32 pages

arxiv created 1998/03/24 · openalex publication_date 1998/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In the limit of ξ≃ a_σ/a_τ→ ∞ the gluodynamics without the magnetic part of action (S_M∼ 1/ξ) is considered as a self-contained model. The model is studied analytically in the continuum limit on an extremely large lattice (N_τ→ ∞ ). Scaling conditions for critical temperature and string tension are considered. The model shows trivial (g²∼ a_τ) asymptotic freedom in the case of continuous gauge groups and nontrivial one (g²∼ 1/ln 1/a_τ) for discrete groups.

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