Spin correlation functions in the Ising model decay exponentially below (and above) the critical temperature, whereas they decay with a power law strictly at the critical temperature. This is a fundamental textbook property of statistical mechanics, so no citation is needed.
The claim describes standard textbook statistical mechanics of the Ising model, where the correlation function decays exponentially (with a mass gap or finite correlation length) in the ordered (low-temperature, T < Tc) and disordered (high-temperature, T > Tc) phases, and only exhibits power-law decay at the critical point Tc. Because this is a well-established foundational fact of the model, it is classified as common knowledge and does not require specific paper citations.