The random lattice as a regularization scheme

1994/05/31 by B. Allés, B. Alles
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #hep-lat

paper · pdf · doi:10.1016/0550-3213(94)00572-v

published as Nucl.Phys. B437 (1995) 627-640 · PostScript file. 22 pages. Revised and enlarged version

arxiv created 1994/12/05 · openalex publication_date 1995/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A semi-analytic method to compute the first coefficients of the renormalization group functions on a random lattice is introduced. It is used to show that the two-dimensional O(N) non-linear σ-model regularized on a random lattice has the correct continuum limit. A degree κ of ``randomness'' in the lattice is introduced and an estimate of the ratio Λ_random/Λ_regular for two rather opposite values of κ in the σ-model is also given. This ratio turns out to depend on κ.

Citations

• Lattice perturbation theory by computer algebra: A three-loop result for the topological susceptibility
• Effect of random defects on the critical behaviour of Ising models