Monte Carlo Investigation of Phase Transitions in the Ising Model under Binary Quenched Bond Disorder (Samarra Journal of Pure and Applied Science, 2026)
The effect of quenched disorder on the critical behavior of the two-dimensional Ising model has been systematically investigated using extensive Monte Carlo simulations and finite-size scaling analysis. To verify the distinctive critical exponents of the pure universality class, the clean 2D Ising system was initially examined. A binary distribution of exchange couplings with different disorder concentrations was then used to introduce disorder, enabling a thorough analysis of its effects on the scaling characteristics close to the critical temperature. Thermodynamic parameters such as correlation length, magnetization, and susceptibility are analyzed, and the results show that disorder contributes significant logarithmic corrections to the scaling laws while the leading critical exponents stay close to those of the clean Ising model. These findings verify that, despite disorder-dependent logarithmic changes to its scaling behavior, the quenched binary Ising model maintains the Ising universality class. Further evidence that weak disorder in two dimensions causes marginally irrelevant perturbations that provide logarithmic corrections to critical scaling is provided by the current results, which are in agreement with theoretical expectations from renormalization-group analysis and earlier numerical investigations.