Hierachical rigidities of glassy systems
Hajime Yoshino, Osaka University
Recent progress of the replica theory for the hardsphere glass in large dimensional limit suggests an intriguing possibility of hierarchical energy landscape reminiscent of spin-glasses . In this talk we argue that response of glasses to external shear would be very similar to the response of spin-glasses to external magnetic field. First we show theoretically that shear-modulus becomes hierarchical reflecting the hierarchical structure of the glass order parameter . Then we discuss our MD simulations which reveal the anticipated difference between « field cooled » (FC) and « zero field cooled » (ZFC) shear-modulus . Finally we show theoretical and numerical suggestions of negatively diverging non-linear shear-modulus associated with the marginal stability of continuous replica symmetry breaking.