Restoration of dimensional reduction in the random-field Ising model at five dimensions

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Disordered Systems

Background:

• The random-field Ising model (RFIM) is a key disordered system for studying critical phenomena.
• Perturbative renormalization group (RG) theory predicts dimensional reduction for RFIM, where D-dimensional critical properties match pure Ising models in D-2 dimensions.
• This prediction fails in low dimensions (e.g., 3D), challenging the validity of perturbative RG.

Purpose of the Study:

• To investigate the validity of dimensional reduction in higher dimensions for the RFIM.
• To precisely determine the critical exponents and renormalization-group invariants of the 5D RFIM at zero temperature.
• To compare the 5D RFIM critical behavior with the pure 3D Ising model.

Main Methods:

• High-precision numerical simulations of the 5D random-field Ising model at zero temperature.
• Analysis of critical exponents, including those related to critical slowing down for ground-state finding algorithms.
• Comparison of universal quantities and probability distributions for different random fields to confirm universality.

Main Results:

• Numerical simulations of the 5D RFIM yield critical exponents statistically consistent with the pure 3D Ising ferromagnet.
• Universality is demonstrated across different random-field distributions.
• The Rushbrooke equality is verified for dimensions 3≤D<6.

Conclusions:

• Dimensional reduction is restored in the 5D random-field Ising model.
• The failure of perturbative RG predictions is a low-dimensional phenomenon.
• These findings validate the RG approach in higher dimensions and provide insights into critical behavior in disordered systems.