Abstract: Our understanding of statistical physics behaviors is rooted in the well-known Ising model, invented in 1920. This mini-course focuses on a disordered version of the one-dimensional Ising model: the ferromagnetic Ising model on a line graph interacting with an external magnetic field, where the field is sampled from an i.i.d. distribution. We will examine the regime where the intensity of the disorder is fixed and the spin-spin interaction goes to infinity. The pure model (where the external field is homogeneous) is well understood. However, introducing disorder complicates the analysis, and we rely on insights from the physics literature to study the model. A key ingredient is a renormalization group introduced by D. S. Fisher, P. Le Doussal and C. Monthus in order to describe the typical configurations under the Gibbs measure. While predictions based on renormalization group theory are usually confirmed through different mathematical methods, this mini-course will present a counterexample where the renormalization group is more accessible and can be effectively exploited. It will also be the occasion to review various concepts used in statistical physics, such as free energy, Glauber dynamics and the role of disorder, alongside techniques such as the transfer matrix formalism and the weak-disorder limit.