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Area of Science:

  • Statistical mechanics
  • Complex systems
  • Information theory

Background:

  • Probabilistic cellular automata model classical spin dynamics.
  • These systems can function as classical memory at low temperatures, even with external magnetic fields.
  • Understanding information stability in noisy systems is crucial for developing robust memory solutions.

Purpose of the Study:

  • To analyze the behavior of the sweep rule, a specific probabilistic cellular automaton.
  • To map the phase diagram of the sweep rule in the temperature (T) and external magnetic field (h) plane.
  • To determine the universality class of the sweep rule.

Main Methods:

  • Analysis of probabilistic cellular automata dynamics.
  • Phase diagram mapping in the (T,h) plane.
  • Universality class identification.

Main Results:

  • A region with two coexisting stable phases was identified in the (T,h) plane for the sweep rule.
  • The sweep rule was found to belong to the weak two-dimensional Ising universality class.
  • Demonstrated the potential for information storage in classical spin models.

Conclusions:

  • The sweep rule exhibits stable phases suitable for information storage.
  • This research contributes to understanding local error correction in complex noisy systems.
  • Findings have implications for developing advanced error-correcting codes, including topological quantum codes.