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The Aizenman--Lieb theorem for the $\mathrm{SU}(2)$ Hubbard model expandsupon the Nagaoka--Thouless theorem for the ground state to encompass finitetemperatures. It can be succinctly stated that the magnetization $m(\beta, b)$of the system in the presence of a field $b$ surpasses the pure paramagneticvalue $m_0(\beta, b)=\tanh(\beta b)$. In this manuscript, we present anextension 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 becomes accessible when expressing the partition function in terms ofpath integrals.

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