Massive modes due to a Higgs-like mechanism for the Boson peak, and Ising-like critical behaviour of glass-forming liquids

We discuss the viscosities, the Ising-like critical behaviour, and the boson peak of supercooled metallic liquids in terms of field-theoretical formulae with local gauge-invariability, which is developed from the Sethna–Sachdev–Nelson gaugeformula. The boson modes around the icosahedral clusters may be attributed to quasi-localised modes, which are created due to absorbing Nambu–Goldstone modes related to zero-modes of three-angle-freedoms of the icosahedral clusters. Furthermore, the present theoretical formula is compared with Elliott's unified model for the boson peak in network glasses. Also, new order parameters for supercooled liquids and glasses are introduced. An analysis from the point of view of the field-theoretical formula is given of experimental viscosity data for bulk metallic glass-forming liquids.