A solvable model in the three-dimensional crystal statistics extension of the spherical model

The author proposes a new solvable model in the crystal statistics, when the spin variables take continuous values similarly to the spherical model, but are restricted by a secondary condition. The thermodynamic functions of the present model in a three-dimensional cubic lattice are evaluated and it is found that there occur two types of phase transitions. The transition of the first type has only one transition temperature Tc and the macroscopic ordering occurs at Tc>T>or=0. In the system of the second type, there are three transition temperatures Tc1, Tc2, Tc3, and the macroscopic ordering mode exists in both temperature regions Tc1>T>Tc2and Tc3>T>or=0. Moreover, the wavenumbers of the macroscopic modes in the region Tc3>T>or=0 of the second type and the region Tc>T>or=0 of the first type varied continuously with change of temperature.