The Field Theory of Specific Heat

Synopsis

A new mathematical approach to condensed matter physics-archive, based on the finite temperature field theory, was recently proposed. The field theory is scale-free formalism, so it denies the absolute scale of thermodynamic temperature and uses dimensionless thermal variables, which are defined by the group velocities of sound and the interatomic distances, combined with the defining constants of the New SI. The universal dimensionless thermal functional is computed and used to derive the specific heat of condensed matter systems. This field theory of specific heat predicts the fourth power of temperature at sufficiently low temperatures, instead of the Debye theory’s cubic law. Experimental data for different condensed matter systems, including diamond lattice crystals, glasses and even solid helium-4, confirm the quartic law. The range of temperatures with the fourth power law varies, thus, it is called the quasi-low temperature regime. The characteristic temperature and the dimensionless parameter of this threshold are explored with the data. The critiques of the Debye theory of specific heat and the Born-von Karman model of lattice dynamics are given.