| Issue |
Europhys. Lett.
Volume 58, Number 6, June 2002
|
|
|---|---|---|
| Page(s) | 806 - 810 | |
| Section | General | |
| DOI | https://doi.org/10.1209/epl/i2002-00445-5 | |
| Published online | 01 June 2002 | |
Vibrational thermodynamic instability of recursive networks
1
Dipartimento di Fisica and INFM,
Università di Parma Parco Area delle Scienze 7/A, 43100 Parma,
Italy
2
Dipartimento di Fisica and INFM, UdR and SMC
Università di Roma “La Sapienza” -
Piazzale A. Moro 2, 00185 Roma, Italy
Received:
26
October
2001
Accepted:
25
March
2002
In this letter we study the thermodynamic stability problem for a
generic geometrical structure by considering the harmonic vibrational
dynamics of a network of masses and springs. We relate the stability
properties of the network to the recurrence properties of random walks
or, equivalently, to the vibrational spectral dimension 
.
This is an extension of the Peierls theorem for the thermodynamic instability
of low-dimensional crystalline structures,
proving that stability is possible if and only if 
.
We predict the existence of an instability critical length
on structurally disordered materials. Our results are discussed on the specific
case of a Sierpinki-gasket fractal, which is exactly solvable.
PACS: 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 61.43.-j – Disordered solids / 65.60.+a – Thermal properties of amorphous solids and glasses: heat capacity, thermal expansion, etc
© EDP Sciences, 2002
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