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

TL;DR

This paper demonstrates that the finite-size scaling function of magnetization in the ferromagnetic Heisenberg chain is universal across different spin magnitudes, supported by analytical and numerical evidence, and links it to correlation function behavior.

Contribution

It provides an explicit analytical form of the universal finite-size scaling function in the classical limit and verifies its universality for quantum spins $S=1/2$ and $1$.

Findings

Explicit classical limit scaling function derived.

Numerical verification for $S=1/2$ and $1$ confirms universality.

Critical exponents determined for the model.

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 finite-size scaling function is given explicitly by an analytical calculation in the classical limit $S=\infty.$ 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.