# Artificial spin ice and vertex models

## TL;DR

This paper reviews the use of vertex models to analyze two-dimensional artificial spin ice systems, highlighting their role in understanding frustrated magnetic interactions in engineered materials.

## Contribution

It provides a summary of recent work on vertex models applied to artificial spin ice, emphasizing their significance in studying frustrated magnetic systems.

## Key findings

- Vertex models effectively describe bidimensional spin-ice samples.
- Artificial spin ice can be engineered with flexible design.
- The work advances understanding of frustration in magnetic materials.

## Abstract

In classical and quantum frustrated magnets the interactions in combination with the lattice structure impede the spins to order in optimal configurations at zero temperature. The theoretical interest in their classical realisations has been boosted by the artificial manufacture of materials with these properties, that are of flexible design. This note summarises work on the use of vertex models to study bidimensional spin-ices samples, done in collaboration with R. A. Borzi, M. V. Ferreyra, L. Foini, G. Gonnella, S. A. Grigera, P. Guruciaga, D. Levis, A. Pelizzola and M. Tarzia, in recent years. It is an invited contribution to a J. Stat. Phys. special issue dedicated to the memory of Leo P. Kadanoff.