The low-temperature thermal properties of amorphous solids, from the tunneling regime to the boson peak (BP), are described in terms of the redistribution of low-energy excitations induced by structural disorder and the progressive loss of vibrational coherence. We develop an interacting two-level-system (ITLS) model based on a coarse-grained three-level Hamiltonian that provides an effective representation of two classes of low-energy excitations: localized tunneling excitations and higher-energy excitations arising from their coupling with elastic vibrations. From the corresponding equilibrium partition functions, we derive the specific heat and construct an effective thermodynamic spectral density that describes the temperature-dependent redistribution of spectral weight between localized and progressively hybridized excitations. Within this picture, the experimentally established excess of vibrational states remains fully consistent with the present description. The ITLS framework further resolves its thermodynamic signature into a low-energy soft contribution, which already develops a boson-peak-like maximum, and higher-energy hybridized contributions that are required to reproduce the complete experimental peak. A finite coherence length $\xi$ introduces an effective cutoff frequency ${\nu }_{\mathrm{off}}$ that delimits the thermodynamically active spectral window. Fits to specific-heat measurements for several glass-forming systems reproduce the experimental behavior over the temperature range considered and yield cutoff frequencies comparable to reported Ioffe–Regel crossover frequencies. Our results provide a unified equilibrium thermodynamic description of the tunneling regime and the boson peak and connect their spectral signatures with the progressive loss of vibrational coherence in disordered solids.

Close

PrevNext

View figure in article

• Specific heat
• Thermal properties
• Glassy systems
• Scaling methods