In a work published in Physical Review Letters (2017) https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.215701 P. Charbonneau and S. Yaida show that the exotic phase transition predicted for infinite-dimensional glassy models can survive down to the physical dimension we live in. The work was notably featured in the following:
https://today.duke.edu/2017/05/breaking-glass-infinite-dimensions
https://gizmodo.com/mathematicians-reignite-thirty-year-old-debate-about-gl-1795758857