An informal introduction to the Parisi formula

TL;DR

This paper provides an informal overview of spin glasses and the Parisi formula, discussing models with incomplete understanding and exploring partial progress through connections with partial differential equations.

Contribution

It offers an accessible introduction to the Parisi formula and highlights ongoing research challenges and approaches involving PDEs.

Findings

Overview of spin glasses and Parisi formula

Discussion of models with limited understanding

Partial progress via PDE connections

Abstract

This note is an informal presentation of spin glasses and of the Parisi formula. We also discuss some models for which the Parisi formula is not well-understood, and some partial progress that relies upon a connection with partial differential equations.