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

TL;DR

This paper develops an exactly solvable mean-field model for disorder-free spin-lattice glass transitions, revealing complex free-energy landscapes and replica symmetry breaking due to spin-lattice coupling.

Contribution

It introduces a higher-dimensional, exactly solvable model extending previous disorder-free spin-glass theories, highlighting the role of spin-lattice interactions.

Findings

Exhibits replica symmetry breaking in the model

Demonstrates complex free-energy landscape

Shows spin-lattice coupling induces glass transition

Abstract

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.