The random lattice as a regularization scheme

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 $\sigma$-model regularized on a random lattice has the correct continuum limit. A degree $\kappa$ of ``randomness'' in the lattice is introduced and an estimate of the ratio ${\Lambda }_{random}/{\Lambda }_{regular}$ for two rather opposite values of $\kappa$ in the $\sigma$-model is also given. This ratio turns out to depend on $\kappa$.

PostScript file. 22 pages. Revised and enlarged version

References in corpus (2)

• Single-Cluster Monte Carlo Study of the Ising Model on Two-Dimensional Random Lattices
• Lattice Perturbation Theory by Computer Algebra: A Three-Loop Result for the Topological Susceptibility

Cited by in corpus (1)

• The 2-dimensional non-linear sigma-model on a random latice