Criticality in diluted ferromagnet

TL;DR

This paper investigates the critical behavior of the mean field diluted Ising ferromagnet using analytical and numerical methods, revealing insights into phase transitions, magnetization scaling, and ergodicity breaking.

Contribution

It provides a comprehensive analysis combining theory, simulations, and prior results to understand phase transitions and critical phenomena in diluted ferromagnets.

Findings

Self-averaging of magnetization established

Explicit free energy expansion near critical line

Agreement between theory, simulations, and previous studies

Abstract

We perform a detailed study of the critical behavior of the mean field diluted Ising ferromagnet by analytical and numerical tools. We obtain self-averaging for the magnetization and write down an expansion for the free energy close to the critical line. The scaling of the magnetization is also rigorously obtained and compared with extensive Monte Carlo simulations. We explain the transition from an ergodic region to a non trivial phase by commutativity breaking of the infinite volume limit and a suitable vanishing field. We find full agreement among theory, simulations and previous results.