The random lattice as a regularization scheme

TL;DR

This paper introduces a semi-analytic method to analyze the renormalization group functions of the 2D O(N) sigma model on a random lattice, demonstrating it maintains the correct continuum limit and exploring how lattice randomness affects key ratios.

Contribution

It presents a novel semi-analytic approach to study the renormalization group on random lattices and shows the model's continuum limit is preserved under this regularization.

Findings

The method computes first coefficients of RG functions on a random lattice.

The 2D O(N) sigma model retains the correct continuum limit on a random lattice.

The ratio of Lambda parameters depends on the degree of lattice randomness.

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 $\kappa$.