It is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin- $S$ Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic. The method of proof is capable of excluding a variety of types of ordering in one and two dimensions.It is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-$S$ Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic. The method of proof is capable of excluding a variety of types of ordering in one and two dimensions.

Physical Review LettersNov 28, 19668,362 citations

Rotated Ferromagnetic Heisenberg Model

Fadi Sun, Jinwu Ye, Wu-Ming Liu

Aug 14, 20140 citations

The 2d/3D Classical Heisenberg Ferromagnet

Robert Goodell Brown, Mikael Ciftan

Springer proceedings in physicsJan 1, 19933 citations

Magnetic Properties of One-Dimensional Ferromagnetic Mixed-Spin Model within Tyablikov Decoupling Approximation

Yuan Chen, Xiang Ying, Chuang-Chuang Song

In this paper, we apply the two-time Green's function method, and provide a simple way to study the magnetic properties of one-dimensional spin-(S,s) Heisenberg ferromagnets. The magnetic susceptibility and correlation functions are obtained by using the Tyablikov decoupling approximation. Our results show that the magnetic susceptibility and correlation length are a monotonically decreasing function of temperature regardless of the mixed spins. It is found that in the case of S=s, our results of one-dimensional mixed-spin model is reduced to be those of the isotropic ferromagnetic Heisenberg chain in the whole temperature region. Our results for the susceptibility are in agreement with those obtained by other theoretical approaches.In this paper, we apply the two-time Green's function method, and provide a simple way to study the magnetic properties of one-dimensional spin-(S,s) Heisenberg ferromagnets. The magnetic susceptibility and correlation functions are obtained by using the Tyablikov decoupling approximation. Our results show that the magnetic susceptibility and correlation length are a monotonically decreasing function of temperature regardless of the mixed spins. It is found that in the case of S=s, our results of one-dimensional mixed-spin model is reduced to be those of the isotropic ferromagnetic Heisenberg chain in the whole temperature region. Our results for the susceptibility are in agreement with those obtained by other theoretical approaches.

Communications in Theoretical PhysicsOct 1, 20104 citations

Conformal symmetry in a two-dimensional Heisenberg ferromagnet

Alexei A. Abrikosov

Journal of Experimental and Theoretical PhysicsDec 1, 19770 citations

It is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-

S

Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic. The method of proof is capable of excluding a variety of types of ordering in one and two dimensions.