Elementary excitations at anomalous interfaces: Dispersion relations from thermodynamics constraints

The dispersion relation, assumed as a power law of a given index, defines the degrees of freedom of elementary excitations. In an anomalous interface, where the degrees of freedom are in principle unspecified, the dispersion relation is determined by thermodynamic constraints. Magnons at the junction between a ferromagnetic material (index 2) and an antiferromagnetic material (index 1) are an explicit example. At high temperatures, the statistically averaged index is 4/3 and varies with temperature. There are large fluctuations at high temperatures and an expression for the lifetime of excitations for any spatial dimension (fractional or not) is proposed.