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