Ergodicity and the Classical Lambda Phi^4 Lattice Field Theory

TL;DR

This paper explores the approach to equilibrium in classical lambda phi^4 lattice field theory, highlighting its pedagogical value for understanding statistical field theory and statistical mechanics, and discussing ergodic and non-ergodic regimes.

Contribution

It provides a detailed analysis of ergodicity in lambda phi^4 theory, connecting numerical and analytical methods with the KAM theorem to understand regime transitions.

Findings

Ergodic and non-ergodic regimes are not sharply separated.

The lambda phi^4 theory serves as a useful pedagogical model.

Connection established between theory and the KAM theorem.

Abstract

In this talk we present some studies in the approach to equilibrium of the classical lambda phi^4 theory on the lattice, giving particular emphasis to its pedagogical usefulness in the context of classical statistical field theory (such as both the analytical and numerical evaluation of correlation functions), as well as in the context of statistical mechanics (such as the equivalence of ensembles in the thermodynamic limit). Since the quartic term could be regarded as a smooth perturbation to the (integrable) gaussian theory, we also discuss the connection of our results with the KAM theorem, showing that the ergodic and non-ergodic regimes are not sharply separated.