Thermal fluctuations, perturbations, QNMs and greybody factor of Letelier black hole surrounded by king dark matter halo

In this paper, we investigate the influence of higher-order thermal fluctuations and perturbations of spin-0 (scalar) and spin-1 (electromagnetic) fields in the background of a Letelier black hole (BH) immersed in a King dark matter (KDM) halo. Within the thermodynamic framework, we analyze how variations in the KDM halo parameters and the surrounding string cloud affect key thermodynamic quantities, including the corrected entropy, corrected heat capacity, and corrected Helmholtz free energy of the BH system. Beyond thermodynamic considerations, we study the dynamical behavior of scalar and electromagnetic fields by deriving their respective perturbation potentials in this BH background. Finally, we compute the quasinormal mode (QNM) spectra for both types of fields and demonstrate how the combined presence of the KDM halo and string cloud modifies the potentials, resulting in shifts of the QNM frequencies and influencing the propagation and decay of spin perturbations.