A finite temperature version of the Nagaoka--Thouless theorem in the \(\mathrm{SU}(n)\) Hubbard model

Abstract

The Aizenman--Lieb theorem for the \(\mathrm{SU}(2)\) Hubbard model extends the Nagaoka--Thouless theorem for the ground state to finite temperatures, and can be stated simply that the magnetization \(m(\beta, b)\) of the system in a field \(b\) exceeds the pure paramagnetic value \(m_0(\beta, b)=\tanh(\beta b)\). In this paper, we present an extension of the Aizenman--Lieb theorem to the \(\mathrm{SU}(n)\) Hubbard model. Our proof relies on a random-loop representation of the partition function, which is available when the partition function is presented in terms of path integrals.