Quantum criticality and percolation in dimer-diluted two-dimensional antiferromagnets

Area of Science:

• Condensed Matter Physics
• Quantum Magnetism
• Statistical Mechanics

Background:

• The S = 1/2 Heisenberg model is a fundamental model in quantum magnetism.
• Previous studies identified a multicritical point in bilayer systems at dimer-dilution percolation.
• Understanding critical phenomena in diluted magnetic systems is crucial.

Purpose of the Study:

• To investigate the S = 1/2 Heisenberg model on single-layer and bilayer square lattices at dimer-dilution percolation points.
• To compare the critical behavior between single-layer and bilayer systems.
• To analyze the magnetic susceptibility and scaling properties.

Main Methods:

• Theoretical study of the S = 1/2 Heisenberg model.
• Analysis of systems at dimer-dilution percolation points (p*).
• Investigation of the critical value g = J2/J1, where J1 and J2 are coupling constants.

Main Results:

• A transition from Néel to disordered ground state occurs at a critical g.
• The multicritical point (g*,p*) found for bilayer systems is absent in single-layer systems.
• Single-layer systems exhibit a line of critical points (g < g*, p*) with continuously varying exponents.
• Uniform magnetic susceptibility diverges as T(-alpha) (alpha in [1/2,1]) in single-layer systems, attributed to an effective free-moment density.
• Bilayer systems show non-divergent susceptibility with robust quantum-critical scaling.

Conclusions:

• Single-layer and bilayer S = 1/2 Heisenberg models exhibit distinct critical behaviors at dimer-dilution points.
• The absence of a multicritical point in single-layer systems leads to unusual magnetic susceptibility scaling.
• Quantum-critical scaling in bilayer systems is remarkably robust, suggesting different underlying physics.