A modified spin-wave theory is applied to the one-dimensional quantum Heisenberg model with long-range ferromagnetic interactions. ( H =- J ∑ i < j ( r i j ) - p S i · S j ). Low-temperature properties of this model are investigated. The susceptibility and the specific heat are calculated; the relation between their behaviors and strength of the long-range interactions is obtained. This model includes both the Haldane-Shastry model and the nearest-neighbor Heisenberg model; the corresponding results in this paper are in agreement with the solutions of both the models. It is shown that there exists an ordering transition at a finite temperature for 1< p <2 where the model has longer-range interactions than the HS model. The critical temperature is estimated.A modified spin-wave theory is applied to the one-dimensional quantum Heisenberg model with long-range ferromagnetic interactions. ( H =- J ∑ i < j ( r i j ) - p S i · S j ). Low-temperature properties of this model are investigated. The susceptibility and the specific heat are calculated; the relation between their behaviors and strength of the long-range interactions is obtained. This model includes both the Haldane-Shastry model and the nearest-neighbor Heisenberg model; the corresponding results in this paper are in agreement with the solutions of both the models. It is shown that there exists an ordering transition at a finite temperature for 1< p <2 where the model has longer-range interactions than the HS model. The critical temperature is estimated.

Journal of the Physical Society of JapanMar 15, 199423 citations

Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models

N. David Mermin, H. Wagner

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

Analytical study of the one-dimensional Heisenberg model

豪加藤

Jan 1, 20040 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.