At low temperatures it is shown theoretically that there exist the singular terms in the magnetic susceptibility of the antiferromagnetic Heisenberg linear chains with spin S =1/2. Furthermore, a discussion is made in analogy with the critical phenomena. The free energy which describes the properties of the present system is composed of two parts: The regular and the singular parts. The singular terms in the magnetic susceptibility come from the latter part.
At low temperatures it is shown theoretically that there exist the singular terms in the magnetic susceptibility of the antiferromagnetic Heisenberg linear chains with spin S =1/2. Furthermore, a discussion is made in analogy with the critical phenomena. The free energy which describes the properties of the present system is composed of two parts: The regular and the singular parts. The singular terms in the magnetic susceptibility come from the latter part.
The nearest-neighbor random-exchange Heisenberg antiferromagnetic Heisenberg chain (s=21) is studied at low temperatures via an approximate renormalization-group method. This entails renormalization of the random-exchange coupling constant J and of the probability law for J. P0(J). After n iterations we find that the renormalized probability function Pn(J(n)), a function of the renormalized coupling J(n), develops singular behavior for small J(n), independent of the initial form of P0(J). This happens both for P0(J) that diverge or go to zero as $J\ensuremath{\rightarrow}0$. The singular form of Pn(J(n)) is such that it leads to a specific heat and susceptibility that behave like $C\ensuremath{\sim}{T}^{1\ensuremath{-}{\ensuremath{\alpha}}_{C}(T)}$ and $\ensuremath{\chi}\ensuremath{\sim}{T}^{\ensuremath{-}{\ensuremath{\alpha}}_{\ensuremath{\chi}}(T)}$. ${\ensuremath{\alpha}}_{C}(T)$ and ${\ensuremath{\alpha}}_{\ensuremath{\chi}}(T)$ are exponents weakly dependent on temperature (T) that go to one as $T\ensuremath{\rightarrow}0$ and satisfy ${\ensuremath{\alpha}}_{\ensuremath{\chi}}(T)>{\ensuremath{\alpha}}_{C}(T)$, for arbitrary initial probability laws. The classical n-vector models, and in particular the classical Heisenberg model are also studied using a renormalization-group approach and it is found that their behavior is different than that of the quantum model: singular behavior in the thermodynamic properties is only obtained if the starting P0(J) is singular. An explanation of these results in terms of the scaling theory of localization is suggested. The relevance of our results to the experimental findings on the magnetic properties of tetracyanoquinodimethanide complexes is also discussed.
Energy spectra and thermodynamic quantities (partition function, entropy, specific heat, susceptibility) of ferrimagnetic Heisenberg chains, made up of two spin sublattices [(1/2-S], are discussed from the exact results computed for finite rings. Extrapolation of the theoretical data versus the length of finite rings N is discussed for S ranging from 1 to (5/2 and compared with previous reported findings for the [(1/2-\ensuremath{\infty}] spin chain. In the low-temperature region, similarities between the ferrimagnetic chains [(1/2-S] and the regular ferromagnetic ones (with spin S-(1/2) are used for the determination of the limiting curves.
A linear chain of S =1/2 spins with the isotropic Hamiltonian H = J Σ( S i x S i +1 x + S i y S i +1 y + S i z S i +1 z -1/4), ( J <0) , at low temperatures is studied numerically by solving a set of nonlinear integral equations which are derived from the Bethe Ansatz. We find that the free energy and susceptibility are both expanded in T/∣J∣ about T =0. The critical exponents are a =-1/2 and y =2. The coefficient of T 3/2 term in the free energy agrees with the spin wave theory with the accuracy of 0.1%. The coefficient of T -2 term in the zero-field susceptibility agrees with Fisher's solution of the classical Heisenberg model with the accuracy of 0.3%. The contribution from the second and higher order terms of the expansions in these thermodynamic quantities is not negligible in the region T /| J |>0.002.
Thermodynamic properties of S=2 antiferromagnetic Heisenberg chains are studied not only under the periodic boundary condition but also under the open one employing a quantum Monte Carlo method. Temperature and size dependences of the energy, the specific heat, and the magnetic susceptibility are calculated and edge effects on them are investigated in detail. The specific heat shows a well-pronounced Schottky anomaly but the maximum is located at a temperature much larger than the Haldane gap of the system. As temperature goes to zero, the magnetic susceptibility vanishes for the periodic chains, while it diverges for the open chains. The edge contribution in the open-chain susceptibility is attributed to the two S=1 effective spins localized at the chain ends at low temperatures, while to an S=2 free spin at high temperatures. This is a visualization of a quantum-classical crossover and an evidence that the present model is a Haldane system. High-temperature behaviors of the thermodynamic quantities are also discussed with the help of a series-expansion method. \textcopyright{} 1996 The American Physical Society.
By the Green’s function method, where spin operators are transformed to fermion operators, an antiferromagnetic Heisenberg chain system has been investigated within the Hartree-Fock approximation. The static correlation ≪SzkSz-k> cannot be reduced to the Ornstein-Zernike form and has no singularity at k=π. The absorption function χzz’’(k,ω) cannot be expressed by the δ-function-like spectrum even at 0°K, but rather by a narrow diffused one, which is due to the two-magnon process. The present dispersion relation has a gap at k=π for T=0°K. The second order phase transition, then, may not occur in the linear chain. The results obtained are discussed comparing with those in the X-Y model and experimental data on TMMC.