We investigate Hg 0.82Re 0.18Ba 2Ca 2Cu 3O 8.76 polycrystalline samples with an optimum oxygen content aimed to analyze both their granular composition and to measure their magnetic response. We find out that the sample corresponds to a solid solution of two intrinsic structural superconductor phases. The AC magnetic susceptibility of a powder sample with a particle size of 20 μm have a critical temperature at 133 K. To make mesoscopic-scale particles of 600 nm in size, a sample of the powder was crushed and sieved. Now, the AC magnetic sample susceptibility shows two critical temperatures at 133 and 98 K. They have been described adopting a particular parametrization of the complex scalar field associated with the order parameter in a new framework of the Ginzburg–Landau theory. Thus, we propose a microscopic model to describe the dynamical interaction between these two types of grains.