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Random fields, topology, and the Imry-Ma argument.

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Summary
This summary is machine-generated.

The study reveals that the behavior of random field models depends on the number of components (n) and dimensions (d). Systems with n ≤ d exhibit strong metastability due to topological defects, while n > d+1 leads to a predictable lowest-energy state.

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Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • Understanding the behavior of systems with quenched disorder is crucial.
  • Topological defects play a significant role in the dynamics of many physical systems.
  • Metastability and glassy behavior are key phenomena in disordered systems.

Purpose of the Study:

  • To investigate the influence of topological defects on the relaxation dynamics and correlation functions.
  • To explore the dimensional and component-number dependence of system behavior in random fields.
  • To characterize the final states and their dependence on initial conditions.

Main Methods:

  • Simulations on large lattices (hundreds of millions of sites).
  • Analysis of spin-spin correlation functions.
  • Study of relaxation dynamics from an initially ordered state.

Main Results:

  • For n ≤ d, topological defects cause strong metastability and initial-condition-dependent final states.
  • For n = d+1, weak metastability is observed.
  • For n > d+1, topological objects are absent, leading to a unique lowest-energy state with exponential correlation decay.

Conclusions:

  • The number of components (n) relative to dimensions (d) dictates the presence and impact of topological defects.
  • Systems with n ≤ d exhibit complex glassy behavior, while higher n values lead to simpler, predictable states.
  • Results align quantitatively with the Imry-Ma argument for higher component numbers.