Universal Finite-Size Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field

Abstract

The finite-size scaling function of the magnetization of the ferromagnetic Heisenberg chain is argued to be universal with respect to the magnitude of the spin. The finitesize scaling function is given explicitly by an analytical calculation in the classical limit S = ∞. The universality is checked for S = 1/2 and 1 by means of numerical calculations. Critical exponents are obtained as well. It is concluded that this universal scaling function originates in the universal behavior of the correlation function.

Universal Finite-Size Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field. II –Nonlinear Susceptibility–

“…(This was partially reported in the previous paper. [5]) We then show that the functionχ 3 obtained for S = ∞ is consistent with numerical data for quantum systems, namely, S = 1/2 and S = 1. Thus we confirm the universality of the scaling function (1.5) up to the third order of x.…”

“…In the previous paper [5] we presented the finite-size scaling function of the linear susceptibility,χ 1 . We used the classical Heisenberg chain to obtain the analytic form ofχ 1 .…”

“…In order to confirm this conjecture for 1 ≤ S < ∞, we have to obtain information from numerical calculations of finite systems, because the Bethe ansatz method is not applicable to higher-spin Heisenberg chains. In the previous paper, [5] we hence generalized the above scaling form It is difficult to obtain the magnetization m(T, h, L) for the classical system. Hence, as the first step, we treated [5] the finite-size scaling form of the linear susceptibility.…”

“…In the previous paper, [5] we hence generalized the above scaling form It is difficult to obtain the magnetization m(T, h, L) for the classical system. Hence, as the first step, we treated [5] the finite-size scaling form of the linear susceptibility. The scaling form (1.5) is followed by the finite-size scaling function of the linear susceptibility χ 1 in the form In the previous paper, [5] we analytically obtained the functionχ 1 for the classical, or the S = ∞ Heisenberg chain with both periodic and open boundary conditions.…”

“…Hence, as the first step, we treated [5] the finite-size scaling form of the linear susceptibility. The scaling form (1.5) is followed by the finite-size scaling function of the linear susceptibility χ 1 in the form In the previous paper, [5] we analytically obtained the functionχ 1 for the classical, or the S = ∞ Heisenberg chain with both periodic and open boundary conditions. Moreover, we showed that the functionχ 1 for S = ∞ fits numerical data for S = 1/2 and S = 1 quite well.…”