Equivalence condition for the canonical and microcanonical ensembles in coupled spin systems

TL;DR

This paper demonstrates that the equivalence of canonical and microcanonical ensembles in coupled spin systems holds even with strong coupling, challenging the common assumption that weak coupling is necessary.

Contribution

It establishes a new condition for ensemble equivalence that does not require weak coupling, expanding the understanding of statistical ensemble validity in spin systems.

Findings

Weak coupling approximation is valid even when coupling strength equals the level spacing.

Ensemble equivalence persists under stronger coupling than traditionally assumed.

Results challenge the necessity of weak coupling for ensemble equivalence.

Abstract

It is typically assumed, without justification, that a weak coupling between a system and a bath is a necessary condition for the equivalence of a canonical ensemble and a microcanonical ensemble. For instance, in a canonical ensemble, temperature emerges if the system and the bath are uncoupled or weakly coupled. We investigate the validity region of this weak coupling approximation, using a coupled composite-spin system. Our results show that the spin coupling strength can be as large as the level spacing of the system, indicating that the weak coupling approximation has a much wider region of validity than usually expected.