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Trajectory phase transitions in noninteracting spin systems.

Loredana M Vasiloiu1,2, Tom H E Oakes1,2, Federico Carollo1,2,3

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|May 20, 2020
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Summary
This summary is machine-generated.

Independent Ising spins show large fluctuations toward order, leading to trajectory phase transitions in the large-deviation regime. This occurs despite noninteracting dynamics, with transitions being continuous or first-order depending on the observable.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems
  • Non-equilibrium Physics

Background:

  • Independent Ising spins typically exhibit disordered behavior.
  • Stochastic dynamics in noninteracting systems are generally simpler to analyze than interacting ones.
  • Large-deviation theory provides tools to study rare events and phase transitions in dynamical systems.

Purpose of the Study:

  • To investigate the emergence of ordered behavior and phase transitions in a system of independent Ising spins.
  • To analyze the large-deviation (LD) regime of stochastic spin dynamics.
  • To explore the duality between spin and plaquette observables in tilted generators.

Main Methods:

  • Studying single spin-flip dynamics at infinite temperature for independent Ising spins.
  • Analyzing time-integrated plaquette observables and their associated tilted generators.
  • Utilizing large-deviation theory to identify phase transitions in trajectory space.
  • Employing analytical methods for pairwise bond observables and numerical simulations for higher-order plaquette observables.

Main Results:

  • A collection of independent Ising spins can exhibit significant fluctuations toward order.
  • A phase transition in trajectory space occurs in the large-deviation regime.
  • The nature of the LD transition depends on the chosen observable: continuous for pairwise bonds and first-order for higher-order plaquettes.
  • An exact spin-plaquette duality was found for the tilted generators.

Conclusions:

  • Noninteracting systems can display complex emergent behavior, including order and phase transitions.
  • The study highlights the power of large-deviation theory in uncovering hidden transitions in dynamical systems.
  • The findings offer insights into the statistical mechanics of non-equilibrium systems and the behavior of complex observables.