  A class of pyrochlore oxides, $A_2$Mo$_2$O$_7$ ($A =$ Ho, Y, Dy, Tb) with
magnetic ions on corner-sharing tetrahedra is known to exhibit spin-glass
transitions without appreciable amount of quenched disorder. Recently a
disorder-free theoretical model for such a system has been proposed which takes
into account not only spins but also lattice distortions as dynamical variables
[K. Mitsumoto, C. Hotta and H. Yoshino, Phys. Rev. Lett. 124, 087201 (2020)].
In the present paper we develop and analyze an exactly solvable disorder-free
mean-field model which is a higher-dimensional counterpart of the model. We
find the system exhibit complex free-energy landscape accompanying replica
symmetry breaking through the spin-lattice coupling.
