Antiferromagnetic Heisenberg spin-1 chain: Magnetic susceptibility of the Haldane chain described using scaling

The phenomenological expression chiT/(Ng(2)mu(B)(2)/k)=C-1n exp(-W-1n/T)+C-2n exp(-W-2n/T) describes very accurately the temperature dependence of the magnetic susceptibility computed for antiferromagnetic rings of Heisenberg spins S=1, whose size n is even and ranges from 6 to 20. This expression has been obtained through a strategy justified by scaling considerations together with finite size numerical calculations. For n large, the coefficients of the expression converge towards C-1=0.125, W-1=0.451J, C-2=0.564, W-2=1.793J (J is the exchange constant), which are appropriate for describing the susceptibility of the spin-1 Haldane chain. The Curie constant, the paramagnetic Curie-Weiss temperature, the correlation length at T=0 and the Haldane gap are found to be closely related to these coefficients. With this expression, a very good description of the magnetic behavior of Y2BaNiO5 and of Ni(C2H8N2)(2)NO2ClO4 (NENP), the archetype of the Haldane gap systems, is achieved over the whole temperature range.