Author:
Jansen Sabine,König Wolfgang,Schmidt Bernd,Theil Florian
Abstract
AbstractWe consider a one-dimensional classical many-body system with interaction potential of Lennard–Jones type in the thermodynamic limit at low temperature $$1/\beta \in (0,\infty )$$
1
/
β
∈
(
0
,
∞
)
. The ground state is a periodic lattice. We show that when the density is strictly smaller than the density of the ground state lattice, the system with N particles fills space by alternating approximately crystalline domains (clusters) with empty domains (voids) due to cracked bonds. The number of domains is of the order of $$N\exp (- \beta e_\mathrm {surf}/2)$$
N
exp
(
-
β
e
surf
/
2
)
with $$e_\mathrm {surf}>0$$
e
surf
>
0
a surface energy. For the proof, the system is mapped to an effective model, which is a low-density lattice gas of defects. The results require conditions on the interactions between defects. We succeed in verifying these conditions for next-nearest neighbor interactions, applying recently derived uniform estimates of correlations.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics
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