WIAS Preprint No. 2789, (2020)

Distribution of cracks in a chain of atoms at low temperature


  • Jansen, Sabine
  • König, Wolfgang
    ORCID: 0000-0002-7673-4364
  • Schmidt, Bernd
  • Theil, Florian

2010 Mathematics Subject Classification

  • 82B21 74B20 74G65 60F10


  • Equilibrium statistical mechanics, atomistic models of elasticity, fracture, lattice gas of defects




We consider a one-dimensional classical many-body system with interaction potential of Lennard--Jones type in the thermodynamic limit at low temperature 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(-β e surf /2) with e surf > 0 a surface energy.

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