Ising spin glass under continuous-distribution random magnetic fields: Tricritical points and instability lines

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Magnetism

Background:

• Spin-glass models are crucial for understanding disordered magnetic systems.
• Random magnetic fields significantly influence the behavior of spin glasses.
• Existing models often simplify random field distributions, limiting applicability to real systems.

Purpose of the Study:

• To investigate the effects of a double Gaussian distribution of random magnetic fields on an infinite-range Ising spin-glass model.
• To explore phase diagrams and critical behaviors, including tricritical points.
• To compare the double Gaussian model with simpler distributions for better theoretical descriptions of real systems.

Main Methods:

• Utilized the replica method within the replica-symmetric solution framework.
• Analyzed the stability of the replica-symmetric solution.
• Derived analytical conditions for the occurrence of tricritical points.

Main Results:

• Phase diagrams exhibit critical frontiers with tricritical points for various sigma values.
• Observed the possibility of two tricritical points along a single critical frontier, a novel finding for continuous random field models.
• Identified the Almeida-Thouless instability at low temperatures and confirmed the stability of the replica-symmetric solution for higher-temperature tricritical points.

Conclusions:

• The double Gaussian random magnetic field model provides a more realistic description of spin-glass systems.
• The presence of multiple tricritical points highlights complex phase transitions not captured by simpler models.
• The findings offer a theoretical basis for interpreting experimental results in disordered magnetic materials.