Low-temperature thermodynamic measurements of single crystals of a series of [Mn₄] networked compounds were performed by the thermal relaxation technique and the ac technique. These materials are constructed by chemical linking of single-molecular magnet (SMM) clusters through coordination bonds and have an intermediate character of SMMs and usual bulk magnetic materials. Each cluster possesses an S ＝ 9 ground state with uniaxial anisotropy dominated by D/k_B ＝ －0.4 ～0.5 K. Because of the existence of a superexchange interaction, J/k_B, between neighboring SMMs, the long-range correlations of large and anisotropic spins have been realized. We have also observed a curious magnetic-field-induced glass-like freezing of spin correlations at low temperatures. The extremely sensitive thermodynamic behavior against the magnetic fields and external pressures were observed by the heat capacity measurements under pressures and with magnetic fields.