Low-temperature thermodynamics of the classical frustrated ferromagnetic chain in magnetic field

TL;DR

This paper analyzes the low-temperature magnetization behavior of a classical frustrated ferromagnetic chain in a magnetic field near a phase transition, revealing universal scaling and the impact of anisotropy.

Contribution

It introduces a universal scaling function for magnetization near the transition point applicable to both classical and quantum models.

Findings

Derived explicit magnetization formulas for low and high fields.

Showed that small anisotropy significantly affects susceptibility near transition.

Linked the partition function to a Schrödinger equation in the scaling limit.

Abstract

Low-temperature magnetization curves of the classical frustrated ferromagnetic chain in the external magnetic field near the transition point between the ferromagnetic and the helical phases is studied. It is shown that the calculation of the partition function in the scaling limit reduces to the solution of the Schr\"{o}dinger equation of the special form for the quantum particle. It is proposed that the magnetization of the classical model in the ferromagnetic part of the phase diagram including the transition point defines the universal scaling function which is valid for quantum model as well. Explicit analytical formulae for the magnetization are given in the limiting cases of low and high magnetic fields. The influence of the easy-axis anisotropy on the magnetic properties of the model is studied. It is shown that even small anisotropy essentially changes the behavior of the susceptibility in the vicinity of the transition point.