Journal of the Physical Society of Japan
Vol. 63 No. 7, July, 1994 pp. 2563-2571
URL : http://jpsj.ipap.jp/link?JPSJ/63/2563/
DOI : 10.1143/JPSJ.63.2563 
The Free Energy and the Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field 
Hiroaki Nakamura and Minoru Takahashi 
Institute for Solid State Physics, University of Tokyo,
Roppongi, Minato-ku, Tokyo 106 
(Received January 22, 1994) 
A nonlinear susceptibilities (the third derivative of a magnetization mS 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 [H =∑Ni=1 {-JSiSi+1-(h/S)Siz},(J>0)] has a scaling relation between mS, h and T: mS(T, h)=F(S2Jh/T2). The scaling function F(x)=(2x/3)-(44x3/135)+ O(x5) is common to all values of spin S. 
KEYWORDS: Bethe Ansatz method, Heisenberg chain, Heisenberg ferromagnet, numerical calculation, scaling function, classical Heisenberg chain, nonlinear susceptibility 
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