자연과학연구논문집

비등방성 결합 교대 =1/2 XY 스핀열의 열역학적 특성

김종재

Published Jan 1, 2011• 0 citations

Abstract

The thermodynamic properties of a trimeric S=1/2 XY spin chain, where unit cells of the ferro-antiferro-antiferromagnetic interaction bonds are displaced alternately, is calculated analytically by using the Jordan-Wigner fermionic transformation. The anisotropy in the coupling bonds causes some unusual characteristics in the specific heat, the magnetization, and the magnetic susceptibility.

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자연과학연구논문집

비등방성 결합 교대 =1/2 XY 스핀열의 열역학적 특성

김종재

Published Jan 1, 2011• 0 citations

OpenAlex

Abstract

Related papers

Thermodynamic Properties of a Linear Antiferromagnetic XY Chain with an Ising Anisotropy

稔次朗田中, Toshijiro Tanaka

Dec 20, 19830 citations

Thermodynamics of spin- 12 tetrameric Heisenberg antiferromagnetic chain

Shou-Shu Gong, Song Wei Gao, Gang Su

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Study of the XY chain with long-range interactions

Acta Physica SinicaJan 1, 20081 citation

Spin-1/2 Antiferromagnetic Heisenberg Chain with Long-range Interactions

Jialiang Li

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The thermodynamic properties of a spin

S=1/2

tetrameric Heisenberg antiferromagnetic chain with alternating interactions

{\text{AF}}_{1}{\text{-AF}}_{2}{\text{-AF}}_{1}\text{-F}

(AF and F denote the antiferromagnetic and ferromagnetic couplings, respectively) are studied by means of the transfer-matrix renormalization-group method and Jordan-Wigner transformation. It is found that in the absence of magnetic field, the thermodynamic behaviors are closely related to the gapped low-lying excitations, and a novel structure with three peaks in the temperature dependence of specific heat is unveiled. In a magnetic field, a phase diagram in the temperature-field plane for the couplings satisfying

{J}_{{\text{AF}}_{1}}={J}_{{\text{AF}}_{2}}={J}_{\text{F}}

is obtained, in which various phases are identified. The temperature dependence of thermodynamic quantities including the magnetization, susceptibility, and specific heat are studied to characterize the corresponding phases. It is disclosed that the magnetization has a crossover behavior at low temperature in the Luttinger liquid phase, which is shown falling into the same class as that in the

S=1

Haldane chain. In the plateau regime, the thermodynamic behaviors alter at a certain field, which results from the crossing of two excitation spectra. By means of the fermion mapping, it is uncovered that the system has four spectra from fermion and hole excitations that are responsible for the observed thermodynamic behaviors.

Linear chains (and rings) of

S=\frac{1}{2}

spins with the anisotropic (Ising-Heisenberg) Hamiltonian $\mathcal{H}=\ensuremath{-}2J\ensuremath{\Sigma}\stackrel{N}{i=1}{{{S}_{i}}^{z}{{S}_{i+1}}^{z}+\ensuremath{\gamma}({{S}_{i}}^{x}{{S}_{i+1}}^{x}+{{S}_{i}}^{y}{{S}_{i+1}}^{y})}\ensuremath{-}g\ensuremath{\beta}\ensuremath{\Sigma}\stackrel{N}{i=1}\mathrm{H}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{S}}_{i}$ have been studied by exact machine calculations for

N=2 \mathrm{to} 11

, $\ensuremath{\gamma}=0 \mathrm{to} 1$ and for ferro- and antiferro-magnetic coupling. The results reveal the dependence on finite size and anisotropy of the spectrum and dispersion laws, of the energy, entropy, and specific heat, of the magnetization and susceptibilities, and of the pair correlations. The limiting $N\ensuremath{\rightarrow}\ensuremath{\infty}$ behavior is accurately indicated, for all $\ensuremath{\gamma}$, in the region

\frac{\mathrm{kT}}{|J|}>~0.5

which includes the maxima in the specific heat and susceptibility. The behavior of thermal and magnetic properties of infinite chains at lower temperatures is estimated by extrapolation. For infinite antiferromagnetic chains the ground-state degeneracy, the anisotropy gap, and the magnetization, perpendicular susceptibility, and pair correlations at

T=0

are similarly studied. Estimates of the long-range order suggest that it vanishes only at the Heisenberg limit $\ensuremath{\gamma}=1$ and confirm the accuracy of Walker's perturbation series in $\ensuremath{\gamma}$.