By Raymond Marie Ferdinand. Houtappel
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Additional resources for Order-Disorder in Hexagonal Lattices
While every honeycomb lattice has a transition temperature, it turns out that there are exceptional triangular lattices for which no transition temperature exists. These are the lattices for which one or all three interactions J i are negative, while all three interactions, or at least the two weakest, are equal in strength. e. JI + J2 > 0, J2 + J3 > 0 and J3 + JI > O. In the latter case Tc will be found from Sh (2JI/kTcl Sh (2J2/kTcl + Sh (2J2/kTc) Sh (2J3/k,Tcl + + Sh (2J3/kTc) Sh (2JI/kTcl = 1.
Hllll + 1121 + 1131) is the energy per atom of the completely ordered state at T = O. 13. Thermodynamic properties ot large isotropic triangular and honeycomb lattices. )t or A4l). e. those with equal interaction I in the three different directions I = II = 12 = 13' An isotropic honeycomb lattice has always a transition temperature, T e, which depends only on the strength III of the interaction by eh (21/kTe) = 2. HOUTAPPEL 28 tion temperature if J is positive. This transition temperature, T c ' is then given by exp (4J1kTc) = 3, (107) as Wan n i e r 7) found already.
K 0 r r i n g a for their stimulating interest and their constant advice, to Mr. T. A. S p r i n g e rand Mr. J. H. v. d. Mer w e for their kind help with some of the calculations and to Mrs. B. Dan i e I s- Hun t for her assistance with the translation into English. I am very grateful to the Lor e n t z Foundation, which enabled me, by a grant, to continue my study of the problem discussed in this article. A. H. 60(1941}252-262. L. 0 n sag e r, Phys. Rev. 65 (1944) 117-149. B. K auf man, Phys.