Trajectory phase transitions and dynamical Lee-Yang zeros of the Glauber-Ising chain

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Researchers

Research units

  • University of Geneva
  • University of Nottingham

Abstract

We examine the generating function of the time-integrated energy for the one-dimensional Glauber-Ising model. At long times, the generating function takes on a large-deviation form and the associated cumulant generating function has singularities corresponding to continuous trajectory (or "space-time") phase transitions between paramagnetic trajectories and ferromagnetically or antiferromagnetically ordered trajectories. In the thermodynamic limit, the singularities make up a whole curve of critical points in the complex plane of the counting field. We evaluate analytically the generating function by mapping the generator of the biased dynamics to a non-Hermitian Hamiltonian of an associated quantum spin chain. We relate the trajectory phase transitions to the high-order cumulants of the time-integrated energy which we use to extract the dynamical Lee-Yang zeros of the generating function. This approach offers the possibility to detect continuous trajectory phase transitions from the finite-time behavior of measurable quantities.

Details

Original languageEnglish
Article number012119
Pages (from-to)1-10
Number of pages10
JournalPhysical Review E
Volume88
Issue number1
Publication statusPublished - 16 Jul 2013
MoE publication typeA1 Journal article-refereed

ID: 4504837