Anomalous thermodynamics of the ferromagnetic p-state clock model on the kagome lattice: An exact analysis within recursive lattice approach

The ferromagnetic p-state clock model on the kagome-like recursive lattice is introduced and its magnetic and thermodynamic properties are analyzed for various values of p up to p=16. It is shown that the model is exactly solvable since the free energy per site of the model can be derived for any given value of p. It is also shown that the model exhibits the second-order phase transitions between the ferromagnetic and paramagnetic phase for all values of p except of p=3, for which the corresponding phase transition is of the first-order type. The equations that drive the positions of all critical temperatures as well as of the transition temperature for p=3 are derived and their numerical values are estimated for all values of p with very high precision. Besides, it is shown that the model exhibits anomalous magnetic and thermodynamic behavior for p≥5 with the presence of the anomalous peak in the low-temperature behavior of the specific heat. Based on the analysis of the corresponding behavior of the entropy and magnetization of the model, it is assumed that this anomalous low-temperature behavior of the specific heat is given by the existence of macroscopically highly-degenerated ground state of the model for p→∞ with nonzero residual entropy.