Four-phonon model of soft-matter quasicrystals for studying thermodynamics

Four-phonon model of soft-matter quasicrystals is proposed, in which there are three solid phonons and one fluid phonon. With this model, the vibration spectrum of soft-matter quasicrystals can be obtained. The generalized Debye frequency, generalized Debye temperature and the thermodynamic functions of soft-matter quasicrystals are observed. The results on the specific heat of soft-matter quasicrystals demonstrate the contributions of both solid phonons and fluid phonon, respectively.