Cluster-size distribution and the magnetic property of a Potts model

Based on the connection between a q-state Potts model (QPM) and a q-state bond-correlated percolation model (QBCPM), we propose that in the calculation of the free energy and a physical quantity, e.g., the magnetic susceptibility, we need only to retain the terms of the most probable cluster-size distribution (MPCSD) defined in the text. For the one-dimensional model, the MPCSD may be calculated exactly. The free energy and the magnetic susceptibility determined by such MPCSD are the same as those calculated exactly by the transfer-matrix method. For the QPM on the lattice with dimensions d≥2, the above assumption about the MPCSD implies that the magnetic susceptibility of the QPM is proportional to the mean cluster sizes of the QBCPM for both T>$T_c$ and T<$T_c$. The hypothesis on the MPCSD may be extended to other spin models. The implication of this work on the theory of the scaling laws of the critical exponents is also discussed.