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arXiv:1110.0771 · Physical Review B

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

Д. В. Дмитриев, V. Ya. Krivnov, N. Yu. Kuzminyh

Published Dec 27, 2011• 4 citations
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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\"odinger 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 the quantum model as well. Explicit analytical formulas 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.

DOI
10.1103/physrevb.84.214438

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The systems exhibiting quantum phase transitions (QPT) are investigated within the Ising model in the transverse field and Heisenberg model with easy-plane single-site anisotropy. Near QPT a correspondence between parameters of these models and of the quantum ${\ensuremath{\varphi}}^{4}$ model is established. A scaling analysis is performed for the ground-state properties. The influence of the external ``longitudinal'' magnetic field on the ground-state properties is investigated, and the corresponding magnetic susceptibility is calculated. Finite-temperature properties are considered with the use of the scaling analysis for the effective classical model proposed by Sachdev. Analytical results for the ordering temperature and temperature dependences of the magnetization and energy gap are obtained in the case of a small ground-state moment. The forms of dependences of observable quantities on the bare splitting (or magnetic field) and renormalized splitting turn out to be different. A comparison with numerical calculations and experimental data on systems demonstrating magnetic and structural transitions (e.g., into a singlet state) is performed.
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Low-temperature magnetic properties of both classical and quantum dimerized ferromagnetic spin chains are studied. It is shown that at low temperatures the classical dimerized model reduces to the classical uniform model with the effective exchange integral ${J}_{0}=J(1\ensuremath{-}{\ensuremath{\delta}}^{2})$, where $\ensuremath{\delta}$ is the dimerization parameter. The partition function and spin correlation function are calculated by means of mapping to the continuum limit, which is justified at low temperatures. The quantum model is studied using the Dyson-Maleev representation of the spin operators. It is shown that in the long-wavelength limit the Hamiltonian of the quantum dimerized chain reduces to that of the uniform ferromagnetic chain with the effective exchange integral ${J}_{0}=J(1\ensuremath{-}{\ensuremath{\delta}}^{2})$. This fact implies that the known equivalence of the low-temperature magnetic properties of classical and quantum ferromagnetic chains remains for the dimerized chains. The considered model is generalized to include the next-neighbor antiferromagnetic interaction.