Loop expansion around the Bethe solution for the random magnetic field Ising ferromagnets at zero temperature

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics

Background:

• The random-field Ising model is crucial for understanding disordered magnetic systems.
• Standard methods like the epsilon expansion face challenges in describing strongly disordered regimes.

Purpose of the Study:

• To develop and apply a novel perturbative loop expansion around the Bethe solution for the random-field Ising model at zero temperature.
• To compare this new expansion with the standard epsilon expansion.

Main Methods:

• Application of a perturbative loop expansion around the Bethe solution.
• Analysis of the random-field Ising model at zero temperature.
• Comparison with the standard epsilon expansion.

Main Results:

• The expansion around the Bethe solution is more suitable for strongly disordered systems and renormalization group (RG) fixed points.
• The new method yields an effective theory with cubic vertices, introducing additional terms absent in the epsilon expansion.
• These additional terms are subdominant, preserving dimensional reduction at this order.

Conclusions:

• The perturbative loop expansion around the Bethe solution offers a more accurate description of disordered systems.
• This approach provides new insights into the behavior of the random-field Ising model near RG fixed points.
• Dimensional reduction remains valid, simplifying analysis even with new cubic vertex contributions.