Continuum limit of field theories regularized on a random lattice

TL;DR

This paper investigates how field theories regularized on random lattices approach the continuum limit, showing that different degrees of randomness are connected through finite renormalizations, thus extending understanding of lattice regularization effects.

Contribution

It demonstrates the existence of the continuum limit on random lattices and establishes the relationship between different randomness parameters via finite renormalizations.

Findings

Continuum limit exists on random lattices.

Different randomness levels are related by finite renormalizations.

Comparison with regular square lattices enhances understanding of regularization effects.

Abstract

The continuum limit and scaling properties of an asymptotically free field theory regularized on a random lattice are compared with those on a regular square lattice. We work on random lattices parametrized by a degree of ``randomness'' $\kappa$. We show that the continuum limit exists and different $\kappa$ are related by a finite renormalization.