1999/03/05 by X. S. Chen, X.S. Chen, V. Dohm · 23 citations
Mathematics · Physics and Astronomy · #Boundary value problem #Cutoff #Geometry #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Periodic boundary conditions #Physics #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Renormalization #Renormalization group #Scaling #Scaling limit #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1007/s100510050901
published in The European Physical Journal B 10(4), 687-703 (Springer Science+Business Media) · LaTex, 51 pages
arxiv created 1999/03/05 · openalex publication_date 1999/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We reexamine the range of validity of finite-size scaling in the ϕ4 lattice model and the ϕ4 field theory below four dimensions. We show that general renormalization-group arguments based on the renormalizability of the ϕ4 theory do not rule out the possibility of a violation of finite-size scaling due to a finite lattice constant and a finite cutoff. For a confined geometry of linear size L with periodic boundary conditions we analyze the approach towards bulk critical behavior as L → ∞ at fixed ξ for T > Tc where ξ is the bulk correlation length. We show that for this analysis ordinary renormalized perturbation theory is sufficient. On the basis of one-loop results and of exact results in the spherical limit we find that finite-size scaling is violated for both the ϕ4 lattice model and the ϕ4 field theory in the region L ≫ ξ. The non-scaling effects in the field theory and in the lattice model differ significantly from each other.