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 $\kappa$.