In this work, the critical behavior and magnetic phase transitions of La0.6Dy0.1Sr0.3Mn−xBixO3 \(\:(\text{x}\:=\:0,\:0.01,\:0.03,\:0.1)\) manganites were systematically investigated. using an iterative fitting procedure based on the Kouvel–Fisher method, critical exponents (β; γ) were determined to be (1.1972; 0.4895), (1.3347; 0.4960), (1.1190; 0.3969) and (1.0743; 0.3890) for \(\:\text{x}=0,\:0.01,\:0.03\:\text{a}\text{n}\text{d}\:0.1\) , respectively. The refined approach ensured improved accuracy by minimizing discrepancies between critical temperatures derived from spontaneous magnetization and inverse susceptibility. The results revealed a crossover in critical behavior, with the exponents deviating from mean-field values, suggesting the presence of short-range magnetic interactions. Through the Landau theory framework, temperature-dependent coefficients \(\:\text{a}\left(\text{T}\right)\) and \(\:\text{b}\left(\text{T}\right)\) were extracted, confirming the stability of the second-order magnetic phase transition. Numerical simulations based on the Landau equation successfully reproduced experimental magnetization isotherms and magnetic entropy changes, showing good agreement, particularly at high fields. This combined experimental and theoretical analysis offers a comprehensive understanding of the influence of Bi substitution on the magnetic criticality and phase transition nature in these manganites.
