Disconnected glass-glass transitions and swallowtail bifurcations in microscopic spin models with facilitated dynamics

TL;DR

This paper explores complex phase transitions, including disconnected glass-glass transitions and bifurcations, in microscopic spin models with facilitated dynamics, extending understanding of dynamic heterogeneity and singularities.

Contribution

It analytically characterizes new phase diagram topologies, including disconnected transitions and swallowtail bifurcations, in spin models with kinetic constraints.

Findings

Identification of disconnected glass-glass transition lines

Analytical determination of phase diagrams for spin mixtures

Prediction of experimental realizations of complex bifurcations

Abstract

It has been recently established that heterogeneous bootstrap percolation and related dynamic facilitation models exhibit a complex hierarchy of continuous and discontinuous transitions depending on lattice connectivity and kinetic constraints. Here the range of the previously observed phase diagram topologies and higher-order singularities is extended to disconnected glass-glass transitions and to cusp and swallowtail bifurcations (which can be generic and degenerate). The phase diagram and the order parameter for two different types of spin mixtures are analytically determined and an experimental realization of the new predictions emerging in our approach is suggested.