Using Bethe ansatz integral equations, we calculate the free energy and susceptibility of spin-$\frac{1}{2}$ one-dimensional Heisenberg ferromagnet $\mathcal{H}{=}J\Sigma(\mbi{S}_{\text{i}}\mbi{S}_{\text{i}+1}-\frac{1}{4})$, ( J <0) at T ≥0.004| J |. We find that the free energy and susceptibility are expanded by $\sqrt{T/|J|}$ at low temperature: $f&=|J|\left\{-1.042\left(\frac{T}{|J|}\right)^{3/2}+1.00\left(\frac{T}{|J|}\right)^{2}-0.9\left(\frac{T}{|J|}\right)^{5/2}+O\left(\frac{T}{|J|}\right)^{3}\right\}\\ \chi&=|J|^{-1}\left\{0.1667\left(\frac{|J|}{T}\right)^{2}+0.581\left(\frac{|J|}{T}\right)^{3/2}+0.68\left(\frac{|J|}{T}\right)^{1}+O\left(\frac{|J|}{T}\right)^{1/2}\right\}.$ The first term of free energy coincides with the spin wave calculation. The first term of susceptibility coincides with Fisher's solution of classical Heisenberg Ferromagnet. We conclude α=-0.5 and γ=2.

Journal of the Physical Society of JapanAug 15, 1985104 citations

Asymptotic Ferromagnetic Ordering of Energy Levels for the Heisenberg Model on Large Boxes

Bruno Nachtergaele, Spitzer, Wolfgang, Shannon L. Starr

arXiv:1509.00907Sep 3, 20151 citation

arXiv:1207.4050 · Journal of Statistical Physics

The Free Energy of the Quantum Heisenberg Ferromagnet at Large Spin

M. Correggi, A. Giuliani

Published Sep 19, 2012• 11 citations

arXiv HTML PDF

DOI: 10.1007/s10955-012-0589-4

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Spin-1/2 One-Dimensional Heisenberg Ferromagnet at Low-Temperature

Minoru Takahashi, Miki Yamada

Using Bethe ansatz integral equations, we calculate the free energy and susceptibility of spin- $\frac{1}{2}$ one-dimensional Heisenberg ferromagnet $\mathcal{H}{=}J\Sigma(\mbi{S}_{\text{i}}\mbi{S}_{\text{i}+1}-\frac{1}{4})$, ( J <0) at T ≥0.004| J |. We find that the free energy and susceptibility are expanded by $\sqrt{T/|J|}$ at low temperature: $f&=|J|\left\{-1.042\left(\frac{T}{|J|}\right)^{3/2}+1.00\left(\frac{T}{|J|}\right)^{2}-0.9\left(\frac{T}{|J|}\right)^{5/2}+O\left(\frac{T}{|J|}\right)^{3}\right\}\\ \chi&=|J|^{-1}\left\{0.1667\left(\frac{|J|}{T}\right)^{2}+0.581\left(\frac{|J|}{T}\right)^{3/2}+0.68\left(\frac{|J|}{T}\right)^{1}+O\left(\frac{|J|}{T}\right)^{1/2}\right\}.$ The first term of free energy coincides with the spin wave calculation. The first term of susceptibility coincides with Fisher's solution of classical Heisenberg Ferromagnet. We conclude α=-0.5 and γ=2.Using Bethe ansatz integral equations, we calculate the free energy and susceptibility of spin-$\frac{1}{2}$ one-dimensional Heisenberg ferromagnet $\mathcal{H}{=}J\Sigma(\mbi{S}_{\text{i}}\mbi{S}_{\text{i}+1}-\frac{1}{4})$, ( J <0) at T ≥0.004| J |. We find that the free energy and susceptibility are expanded by $\sqrt{T/|J|}$ at low temperature: $f&=|J|\left\{-1.042\left(\frac{T}{|J|}\right)^{3/2}+1.00\left(\frac{T}{|J|}\right)^{2}-0.9\left(\frac{T}{|J|}\right)^{5/2}+O\left(\frac{T}{|J|}\right)^{3}\right\}\\ \chi&=|J|^{-1}\left\{0.1667\left(\frac{|J|}{T}\right)^{2}+0.581\left(\frac{|J|}{T}\right)^{3/2}+0.68\left(\frac{|J|}{T}\right)^{1}+O\left(\frac{|J|}{T}\right)^{1/2}\right\}.$ The first term of free energy coincides with the spin wave calculation. The first term of susceptibility coincides with Fisher's solution of classical Heisenberg Ferromagnet. We conclude α=-0.5 and γ=2.

Journal of the Physical Society of JapanAug 15, 1985104 citations

Asymptotic Ferromagnetic Ordering of Energy Levels for the Heisenberg Model on Large Boxes

Bruno Nachtergaele, Spitzer, Wolfgang, Shannon L. Starr

We prove a result for the spin- $1/2$ quantum Heisenberg ferromagnet on $d$ -dimensional boxes $\{1,\dots,L\}^d \subset \mathbb{Z}^d$ . For any $n$ , if $L$ is large enough, the Hamiltonian satisfies: among all vectors whose total spin is at most $(L^d/2)-n$ , the minimum energy is attained by a vector whose total spin is exactly $(L^d/2)-n$ .We prove a result for the spin-$1/2$ quantum Heisenberg ferromagnet on $d$-dimensional boxes $\{1,\dots,L\}^d \subset \mathbb{Z}^d$. For any $n$, if $L$ is large enough, the Hamiltonian satisfies: among all vectors whose total spin is at most $(L^d/2)-n$, the minimum energy is attained by a vector whose total spin is exactly $(L^d/2)-n$.

arXiv:1509.00907Sep 3, 20151 citation

Using Bethe ansatz integral equations, we calculate the free energy and susceptibility of spin-

\frac{1}{2}

one-dimensional Heisenberg ferromagnet $\mathcal{H}{=}J\Sigma(\mbi{S}_{\text{i}}\mbi{S}_{\text{i}+1}-\frac{1}{4})$, ( J <0) at T ≥0.004| J |. We find that the free energy and susceptibility are expanded by

\sqrt{T/|J|}

at low temperature: $f&=|J|\left\{-1.042\left(\frac{T}{|J|}\right)^{3/2}+1.00\left(\frac{T}{|J|}\right)^{2}-0.9\left(\frac{T}{|J|}\right)^{5/2}+O\left(\frac{T}{|J|}\right)^{3}\right\}\\ \chi&=|J|^{-1}\left\{0.1667\left(\frac{|J|}{T}\right)^{2}+0.581\left(\frac{|J|}{T}\right)^{3/2}+0.68\left(\frac{|J|}{T}\right)^{1}+O\left(\frac{|J|}{T}\right)^{1/2}\right\}.$ The first term of free energy coincides with the spin wave calculation. The first term of susceptibility coincides with Fisher's solution of classical Heisenberg Ferromagnet. We conclude α=-0.5 and γ=2.

We prove a result for the spin-

1/2

quantum Heisenberg ferromagnet on

d

-dimensional boxes

\{1,\dots,L\}^d \subset \mathbb{Z}^d

. For any

n

, if

L

is large enough, the Hamiltonian satisfies: among all vectors whose total spin is at most

(L^d/2)-n

, the minimum energy is attained by a vector whose total spin is exactly

(L^d/2)-n