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

Abstract

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
Volume56
Issue number12
DOIs
StatePublished - 24 Mar 2023

Keywords

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

Fingerprint

Dive into the research topics of 'Contact geometric approach to Glauber dynamics near a cusp and its limitation'. Together they form a unique fingerprint.

Cite this