Universality from disorder in the random-bond Blume-Capel model

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• The Blume-Capel model describes magnetic systems with crystal-field interactions.
• Understanding the impact of quenched disorder on phase transitions is crucial in statistical mechanics.
• Previous studies explored pure Blume-Capel models; this work investigates disorder effects.

Purpose of the Study:

• To investigate the influence of quenched disorder in exchange couplings on the Blume-Capel model.
• To determine the universality class of the disordered Blume-Capel model.
• To analyze the behavior of correlation length, susceptibility, and specific heat under disorder.

Main Methods:

• High-precision Monte Carlo simulations were employed.
• Finite-size scaling analysis was used to study critical phenomena.
• The study focused on the Blume-Capel model on a square lattice.

Main Results:

• Quenched disorder softens first-order transitions to continuous transitions, leading to a divergent correlation length.
• The disordered system belongs to the Ising model universality class with logarithmic corrections.
• Finite-size scaling in the pre-transition regime exhibits transient effects with a crossover length scale L* ≈ 32.

Conclusions:

• Disorder fundamentally alters the phase transition nature in the Blume-Capel model.
• The observed universality class suggests a connection to other disordered magnetic systems.
• Transient effects in finite-size scaling provide insights into the crossover behavior in disordered systems.