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Ising spin glass in a random network with a Gaussian random field.

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We explored thermodynamic phase transitions in spin glass (SG) and random field (RF) systems using a random graph model. Our findings reveal distinct behaviors compared to mean-field theory, especially concerning replica symmetric solution stability.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Disordered Systems

Background:

  • Thermodynamic phase transitions are crucial for understanding material properties.
  • Spin glass (SG) and random field (RF) systems exhibit complex behaviors due to quenched disorder.
  • Mean-field theory provides a simplified view, often neglecting network connectivity effects.

Purpose of the Study:

  • To investigate thermodynamic phase transitions in the combined presence of spin glass and random field effects.
  • To analyze the influence of network connectivity on these transitions using a random graph model.
  • To compare the findings with predictions from mean-field theory.

Main Methods:

  • Utilized a random graph model to simulate quenched disorder and controllable connectivity.
  • Employed the replica symmetric (RS) approximation for theoretical analysis.
  • Assessed the stability of the RS solution using the two-replica method.

Main Results:

  • Identified differences between the random graph model and fully connected mean-field theory.
  • Demonstrated that for low connectivity, the RS solution remains stable above a critical magnetic field, irrespective of RF strength.
  • Observed distinct crossover behaviors between RF and SG regimes compared to mean-field predictions.

Conclusions:

  • Network connectivity significantly alters thermodynamic phase transitions in SG-RF systems.
  • The replica symmetric solution's stability is dependent on connectivity, offering new insights beyond mean-field approximations.
  • This study highlights the importance of network structure in understanding disordered magnetic systems.