Dimensional reduction breakdown and correction to scaling in the random-field Ising model.

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Quantum Field Theory

Background:

• The random-field Ising model (RFIM) exhibits complex critical behavior influenced by disorder.
• Dimensional reduction and supersymmetry are key concepts in understanding critical phenomena in certain dimensions.
• The transition at dDR≈5.1 marks a significant change in the RFIM's critical properties.

Purpose of the Study:

• To theoretically analyze corrections to scaling in the RFIM near dDR≈5.1.
• To investigate the breakdown of supersymmetry and dimensional reduction in the RFIM.
• To elucidate the boundary-layer mechanism responsible for the emergence of a new fixed point.

Main Methods:

• Nonperturbative functional renormalization group (NP-FRG) calculations.
• Theoretical analysis of critical exponents and scaling behavior.
• Comparison with large-scale lattice simulations.

Main Results:

• NP-FRG results show excellent agreement with d=5 lattice simulations of the RFIM.
• Detailed the leading correction-to-scaling exponent.
• Identified the boundary-layer mechanism governing the transition between different critical regimes.

Conclusions:

• The study provides a robust theoretical framework for understanding RFIM critical behavior.
• Confirms the breakdown of supersymmetry and dimensional reduction below dDR≈5.1.
• Offers insights into the complex interplay of disorder and dimensionality in critical systems.