The method of Mermin and Wagner [Phys. Rev. Lett. 17, 1133 (1966)] is used to show that one- and two-dimensional spin systems interacting with a general isotropic interaction H=1/2 Σ ijn ℐij (n) (Si·Sj)n, where the exchange interactionsIij(n) are of finite range, cannot order in the sense that 〈Oi〉=0 for all traceless operators Oi defined at a single site i. Mermin and Wagner have proved the above for the case n = 1 with Oi = Si, i.e., for the Heisenberg Hamiltonian. The proof allows us to rule out the possibility that a small isotropic biquadratic exchange (Si·Sj) 2 could induce ferromagnetism or antiferromagnetism in a two-dimensional Heisenberg system.
ASJC Scopus subject areas
- Physics and Astronomy(all)