# Dilution of Ferromagnets via a Random Graph-based Strategy

## TL;DR

This paper introduces a Monte Carlo method using modified Erdős-Rényi graphs to model the dilution of high-dimensional ferromagnets, enabling efficient simulation and analysis of their properties and equilibria.

## Contribution

It presents a novel graph-based Monte Carlo approach for simulating ferromagnet dilution, applicable to high-dimensional models and complex networks.

## Key findings

- Efficient simulation of continuous dilution process.
- Analysis of equilibrium properties of diluted ferromagnets.
- Potential applications in complex network modeling.

## Abstract

The dynamics and behavior of ferromagnets have a great relevance even beyond the domain of statistical physics. In this work, we propose a Monte Carlo method, based on random graphs, for modeling their dilution. In particular, we focus on ferromagnets with dimension $D \ge 4$, which can be approximated by the Curie-Weiss model. Since the latter has as graphic counterpart a complete graph, a dilution can be in this case viewed as a pruning process. Hence, in order to exploit this mapping, the proposed strategy uses a modified version of the Erd\H{o}s-Renyi graph model. In doing so, we are able both to simulate a continuous dilution, and to realize diluted ferromagnets in one step. The proposed strategy is studied by means of numerical simulations, aimed to analyze main properties and equilibria of the resulting diluted ferromagnets. To conclude, we also provide a brief description of further applications of our strategy in the field of complex networks.