Evidence for Supersymmetry in the Random-Field Ising Model at D=5.

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• High-Energy Physics

Background:

• Supersymmetry (SUSY) posits a relationship between bosons and fermions.
• Disordered systems, like the random-field Ising model, exhibit complex behavior.
• SUSY offers potential simplifications for studying such systems.

Purpose of the Study:

• To conduct a rigorous numerical test of supersymmetry in the random-field Ising model.
• To investigate the validity of SUSY predictions relating disordered and clean systems.
• To explore the dimensional dependence of these supersymmetric relationships.

Main Methods:

• Extensive zero-temperature numerical simulations.
• Finite-size scaling analysis to check theoretical relationships.
• High-accuracy computational testing of correlation functions.

Main Results:

• Supersymmetric predictions are accurately satisfied in five spatial dimensions (D=5).
• These predictions fail to describe the model's behavior at four spatial dimensions (D=4).
• Demonstrates a critical dimensional dependence for SUSY in this model.

Conclusions:

• The study provides a nontrivial validation of supersymmetry in disordered systems at D=5.
• Highlights the limitations of current supersymmetric predictions at lower dimensions (D=4).
• Suggests further theoretical and numerical investigations into dimensional effects on supersymmetry.