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

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.