Replica theory for disorder-free spin-lattice glass transition on a treelike simplex network

A class of pyrochlore oxides, A2Mo2O7 (A = Ho, Y, Dy, Tb), with magnetic ions on corner-sharing tetrahedra is known to exhibit spin glass transitions without an 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 [Mitsumoto, Hotta, and Yoshino, Phys. Rev. Lett. 124, 087201 (2020)]. In this 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 exhibits a complex free-energy landscape accompanying replica symmetry breaking through the spin-lattice coupling.