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

Abstract

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 $p\ge 5$ 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 $p\to \infty$ with nonzero residual entropy.