Spin-1/2 One-Dimensional Heisenberg Ferromagnet at Low-Temperature
Spin-1/2 One-Dimensional Heisenberg Ferromagnet at Low-Temperature
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Spin-1/2 一维海森堡低温铁磁体
DOI：
10.1143/jpsj.54.2808
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发表时间：
1985
影响因子：
1.7
通讯作者：
Miki Yamada
中科院分区：
文献类型：
--
作者：
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.