Low-frequency vibrational spectrum and low-temperature specific heat of Bethe lattices
- 1 January 1992
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 45 (1) , 454-455
- https://doi.org/10.1103/physrevb.45.454
Abstract
By mapping the harmonic-oscillations equations onto the random-walk equations, we calculate analytically the low-frequency vibrational spectrum of a Bethe lattice and show that it has a gap between zero frequency and a critical frequency. Using these results, we then obtain a low-temperature asymptotic expression for the vibrational specific heat and find that it goes exponentially to zero as T→0.Keywords
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