Contact geometric approach to Glauber dynamics near a cusp and its limitation

Shin Itiro Goto*, Shai Lerer, Leonid Polterovich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study a nonequilibrium mean field Ising model in the low temperature phase regime, where metastable equilibrium states develop a cuspidal (spinodal) singularity. We focus on celebrated Glauber dynamics, and design a contact Hamiltonian flow which captures some of its rough features in this regime. We prove, however, that there is an inevitable discrepancy between the scaling laws for the relaxation time in the Glauber and the contact Hamiltonian dynamical systems.

Original languageEnglish
Article number125001
JournalJournal of Physics A: Mathematical and Theoretical
Issue number12
StatePublished - 24 Mar 2023


FundersFunder number
Japan Society for the Promotion of ScienceJP19K03635
Israel Science Foundation1102/20
Technion-Israel Institute of Technology


    • Glauber dynamics
    • Ising model
    • contact geometry
    • cuspidal singularity
    • relaxation process


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