More on random-lattice fermions

TL;DR

This paper investigates the effects of random lattice structures on fermion determinants, revealing that certain random lattices may eliminate fermion doubling, unlike traditional lattice formulations, with implications for lattice gauge theories.

Contribution

It compares two types of random lattices and shows that one may avoid fermion doubling, challenging previous assumptions about randomness always removing doublers.

Findings

Fermion doubling confirmed on one lattice type

Possible absence of doubling on the other lattice type in 2D

Randomness alone does not guarantee removal of fermion doublers

Abstract

The lattice fermion determinants, in a given background gauge field, are evaluated for two different kinds of random lattices and compared to those of naive and wilson fermions in the continuum limit. While the fermion doubling is confirmed on one kind of lattices, there is positive evidence that it may be absent for the other, at least for vector interactions in two dimensions. Combined with previous studies, arbitrary randomness by itself is shown to be not a sufficient condition to remove the fermion doublers.