• Media type: E-Article
  • Title: Order—Disorder Phenomena. II. Elastic Constants of a Two-Dimensional Ising Model
  • Contributor: Renard, Rémi; Garland, Carl W.
  • Published: AIP Publishing, 1966
  • Published in: The Journal of Chemical Physics
  • Extent: 1125-1129
  • Language: English
  • DOI: 10.1063/1.1726797
  • ISSN: 1089-7690; 0021-9606
  • Keywords: Physical and Theoretical Chemistry ; General Physics and Astronomy
  • Abstract: <jats:p>The mechanical behavior of an Ising model in which the spins are located on the particles of a compressible lattice has been investigated. Analytical expressions are derived for the spin contribution to all three independent elastic constants of a square ferromagnetic system. It is found that the constant area temperature dependence of c11 (the compressional stiffness constant) is dominated by a term proportional to the configurational specific heat. In contrast, the angle shear constant (denoted by c44) has a spin contribution which is directly proportional to the Ising internal energy. The other shear constant C′ is a more complicated function of temperature, but it is similar to c44 in that both constant-area shear constants have an inflection point of infinite slope at Tc.</jats:p>
  • Description: <jats:p>The mechanical behavior of an Ising model in which the spins are located on the particles of a compressible lattice has been investigated. Analytical expressions are derived for the spin contribution to all three independent elastic constants of a square ferromagnetic system. It is found that the constant area temperature dependence of c11 (the compressional stiffness constant) is dominated by a term proportional to the configurational specific heat. In contrast, the angle shear constant (denoted by c44) has a spin contribution which is directly proportional to the Ising internal energy. The other shear constant C′ is a more complicated function of temperature, but it is similar to c44 in that both constant-area shear constants have an inflection point of infinite slope at Tc.</jats:p>
  • Footnote: