Daniel Stein - NYU
Wednesday, February 11, 2026
Zoom opens: 10:30AM EST
Seminar begins: 10:45AM EST
Ground State Excitations and the Nature of the Spin Glass Phase
The thermodynamics of spin glasses, and more generally the statistical mechanics of quenched disorder, is a problem of general interest to physicists and mathematicians from multiple disciplines and backgrounds. Its importance was recognized in 2021 with the awarding of the Nobel Prize in Physics to Giorgio Parisi for his replica symmetry breaking solution of the Sherrington-Kirkpatrick model (a mean-field model of spin glasses) and its application to other problems
in complex systems.
In this talk we will focus on the stability of ground states in the classical Edwards-Anderson Ising spin glass in dimensions two and higher against perturbations of a single coupling. After reviewing some basic concepts (in particular metastates, critical droplets, and flexibilities) and proposed scenarios for the low-temperature spin glass phase, we will show how ground state stability is related to fluctuations in the energy difference, restricted to finite volumes, between two infinite-volume spin glass ground states. We find that if incongruent ground states exist in any dimension, these fluctuations grow with the volume. These results are used to prove that in the appropriate setting the two-dimensional Edwards-Anderson Ising spin glass has just a single pair of globally spin-reversed ground states. We further show that a type of excitation above a ground state, whose interface with the ground state is space-filling and whose energy remains O(1) independently of the volume, cannot exist in any dimension.