Complexes of Several Spins in a Linear Heisenberg Chain

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 $S.$ 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 $S.$

arXiv:cond-mat/9401074Journal of the Physical Society of JapanJul 15, 199420 citations

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.