Percolation of Fortuin-Kasteleyn clusters for the random-bond Ising model

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• The 3D ±1 random-bond Ising model exhibits complex magnetic behavior dependent on temperature and antiferromagnetic bond concentration.
• Ground states transition from ferromagnetic to spin-glass phases at a critical concentration p_c ≈ 0.222.
• Understanding phase transitions and universality classes is crucial in statistical physics.

Purpose of the Study:

• To investigate the percolation transition of Fortuin-Kasteleyn clusters in the 3D ±1 random-bond Ising model.
• To determine the relationship between the percolation transition temperature and the magnetic ordering temperature.
• To analyze the universality of the percolation transition across different ground states and bond concentrations.

Main Methods:

• Application of generalized Swendson-Wang and Wolff cluster algorithms.
• Construction of Fortuin-Kasteleyn clusters.
• Simulations performed on large system sizes up to N=200^3 spins.

Main Results:

• The Fortuin-Kasteleyn percolation transition temperature consistently exceeds the magnetic ordering temperature for p > 0.
• Evidence suggests this difference exists even for small concentrations of negative bonds.
• For p > 0, the percolation transition appears universal and belongs to the standard percolation universality class, regardless of ground state order.

Conclusions:

• Fortuin-Kasteleyn cluster percolation is generally distinct from magnetic ordering in this model.
• Bond occupancy correlations within clusters are irrelevant for universality, except at p=0.
• At p=0, the percolation transition aligns with the Ising universality class due to direct ties to Ising correlations.