  The Kondo lattice model (KLM) is a typical model describing heavy fermion
systems. In this paper, we consider the interaction of phonons with the system
described by the one-electron KLM. Magnetic properties of the ground state of
this model are revealed in a rigorous form. Furthermore, we derive the
effective Hamiltonian in the strong coupling limit ($J\to \infty$) for the
strength of the spin-exchange interaction $J$; we examine the magnetic
properties of the ground state of the effective Hamiltonian and prove that the
Aizenman--Lieb theorem concerning the magnetization holds for the effective
Hamiltonian at finite temperatures. Generalizing the obtained results, we
clarify a mechanism for the stability of magnetic properties of the ground
state in the one-electron KLM system.
