The Free Energy and the Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field

Details The Free Energy and the Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field The Free Energy and the Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field

1994-01-31

arxiv.org/abs/cond-mat/9401074v1

Journal of the Physical Society of Japan, 63, 2563 (1994)

Physics

Condensed Matter

16 pages (revtex 2.0) + 6 PS figures upon request

Scientific paper

A nonlinear susceptibilities (the third derivative of a magnetization $m_S$ by a magnetic field $h$ ) of the $S$=1/2 ferromagnetic Heisenberg chain and the classical Heisenberg chain are calculated at low temperatures $T.$ In both chains the nonlinear susceptibilities diverge as $T^{-6}$ and a linear susceptibilities diverge as $T^{-2}.$ The arbitrary spin $S$ Heisenberg ferromagnet $[$ ${\cal H} = \sum_{i=1}^{N} \{ - J{\bf S}_{i} {\bf S}_{i+1} - (h/S) S_{i}^{z} \}$ $(J>0),$ $]$ has a scaling relation between $m_S,$ $h$ and $T:$ $m_S(T,h) = F( S^2 Jh/T^2).$ The scaling function $F(x)$=(2$x$/3)-(44$x^{3}$/135) + O($x^{5}$) is common to all values of spin $S.$

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