Phase Transitions, Geodesic Structure, and Thermodynamic Properties Measurement of Einstein-Maxwell-Power Yang-Mills Black Hole Models
In this work, we test the geometrical structure and thermodynamic properties of the Einstein-Maxwell-Power-Yang-Mills black hole (BH) models, which constitute a nonlinear generalization of the standard Einstein-Yang-Mills theory through the inclusion of a power-law Yang-Mills invariant. Also, we begin by analyzing the spacetime geometry via the metric function $f(r)$ and examine the modifications induced by the electromagnetic charge and nonlinear Yang-Mills parameter on the horizon structure, causal structure, and gravitational potential. Subsequently, the dynamics of photons and massive particles are explored through the study of null and timelike geodesics, allowing the determination of the effective potential, photon sphere radius, and associated BH shadow. Also, the stability of circular photon orbits is quantified using the Lyapunov exponent, which characterizes the timescale of orbital instability and provides a direct link to observable photon ring features. For massive particles, the innermost stable circular orbit (ISCO) is calculated, illustrating the influence of BH parameters on the dynamics of accretion disks. From the thermodynamic viewpoint, we compute the principal thermodynamic quantities, including the BH mass, Hawking temperature, Bekenstein-Hawking entropy, heat capacity, and Gibbs free energy, to assess both local and global stability of the system. The divergence of the heat capacity signals the occurrence of second-order phase transitions, whereas the Gibbs free energy analysis identifies possible first-order phase transitions between distinct thermodynamic configurations. In this context, our results demonstrate that the nonlinear Yang-Mills parameter strongly affects the spacetime geometry, particle dynamics, and thermodynamic phase structure, shifting the location of stability regions and critical points associated with phase transitions.