Monte Carlo study of the triangular Blume-Capel model under bond randomness

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• The Blume-Capel model is a key system for studying magnetic phase transitions.
• Understanding the impact of disorder on universality classes is crucial in statistical mechanics.
• Previous studies have explored disorder effects in various lattice models.

Purpose of the Study:

• To investigate the influence of bond randomness on universality in the 2D Blume-Capel model.
• To determine the universality class of phase transitions under quenched disorder.
• To compare the behavior with other models like the Ising and Potts models.

Main Methods:

• Numerical simulations using finite-size scaling analysis.
• Focus on a two-dimensional triangular lattice.
• Analysis across both first- and second-order phase transition regimes.

Main Results:

• Second-order phase transitions under bond randomness align with the 2D random Ising model universality class.
• Transitions originating from the pure model's first-order regime also exhibit this universality.
• Findings support strong universality in 2D Ising models with quenched disorder.

Conclusions:

• The 2D Blume-Capel model with bond disorder demonstrates behavior consistent with the 2D random Ising universality class.
• This universality holds even when transitions emerge from the first-order regime, differing from Potts model behavior.
• Results corroborate existing renormalization-group calculations for disordered Blume-Capel models.