The Néel temperature, TN, of quasi-one-and quasi-two-dimensional antiferromagnetic Heisenberg models on a cubic lattice is calculated by Monte Carlo simulations as a function of inter-chain (interlayer) to intra-chain (intra-layer) coupling J ′ /J down to J ′ /J ≃ 10 −3 . We find that TN obeys a modified random-phase approximation-like relation for small J ′ /J with an effective universal renormalized coordination number, independent of the size of the spin. Empirical formulae describing TN for a wide range of J ′ and useful for the analysis of experimental measurements are presented.While genuinely one-dimensional (1D) and two-dimensional (2D) antiferromagnetic Heisenberg (AFH) models cannot display long-range order (LRO) except at zero temperature [1], weak inter-chain or inter-layer couplings, J ′ , which always exist in real materials, lead to a finite Néel temperature T N . So far, the J ′ -dependence of T N was calculated by exactly treating effects of the strong interaction J in the 1D or 2D system, but using mean-field approximations for the inter-chain and interlayer coupling. Recently, more advanced theories of the latter effects have been proposed for quasi-1D (Q1D) [3,4] and quasi-2D (Q2D) [5] systems, and the results have been compared with the experimental observations on Q1D antiferromagnets, e.g., Sr 2 CuO 3 [6], and Q2D antiferromagnets, e.g., La 2 CuO 4 [7]. In view of the importance of experimentally well-studied Q2D antiferromagnets as undoped parent compounds of the high-temperature superconductors, accurate and unbiased numerical results for Q1D and Q2D AFH models are strongly desired. In a recent work along this line, Sengupta et al. [8] have demonstrated peculiar temperature dependences of the specific heat in the quantum Q2D AFH model.Here we calculate the Néel temperature T N as a function of J ′ in fully three-dimensional (3D) classical and quantum Monte Carlo (MC) simulations of coupledchains and coupled-layers. Our MC results on the quantum spin-S and classical S = ∞ AFH models are analyzed by a modified random-phase approximation (RPA) with a renormalized coordination number defined bywhere χ s (T ) is the staggered susceptibility of the 1D or 2D model at temperature T . In a simple RPA calculation [2], this quantity is just the coordination number z d in the inter-chain or inter-layer directions: z 1 = 4 and z 2 = 2 for the Q1D and Q2D systems, respectively. Our main result is that ζ(J ′ ) evaluated by Eq. (1) with our numerically obtained T N (J ′ ) and χ s (T ) becomes constant, with the constants k 1 = 0.695 and k 2 = 0.65. These constants k d differ from the simple RPA result k d = 1, but the value of k 1 is consistent with the modified self-consistent RPA theory for the quantum Q1D (q-Q1D) model of Irkhin and Katanin (IK) [3]. Furthermore we find, that, within our numerical accuracy, the value of k d is the same for the S = 1/2, S = 1, S = 3/2 and S = ∞, and we conjecture that k d is universal and independent of the spin S for small J ′ /J. We also propose empirical formulae ...
The S = 1/2 and S = 1 two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works. It is confirmed that the quantum critical phenomena on the phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for S = 1, we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchaincoupling, case.
Ground-state properties of the spin-1 two-leg antiferromagnetic ladder are investigated precisely by means of the quantum Monte Carlo method. It is found that the correlation length along the chains and the spin gap both remain finite regardless of the strength of interchain coupling, i.e., the Haldane state and the spin-1 dimer state are connected smoothly without any quantum phase transitions between them. We propose a plaquette-singlet solid state, which qualitatively describes the ground state of the spin-1 ladder quite well, and also a corresponding topological hidden order parameter. It is shown numerically that the new hidden order parameter remains finite up to the dimer limit, though the conventional string order defined on each chain vanishes immediately when infinitesimal interchain coupling is introduced.
A new wavefunction which improves the Gutzwiller-type local ansatz method has been pro- Furthermore, the present approach combined with the projection operator method CPA is shown to describe quantitatively the excitation spectra in the insulator regime as well as the critical Coulomb interactions for a gap formation in infinite dimensions.
Differential scanning calorimetry, thermogravimetric-differential thermal analysis, and X-ray diffraction measurements were performed on single crystals of L(+)-tartaric, D(-)-tartaric, and monohydrate racemic (MDL-) tartaric acid. The exact crystal structures of the three acids, including the positions of all hydrogen atoms, were determined at room temperature. It was pointed out that one of O-H-O hydrogen bonds in MDL-tartaric acid has an asymmetric double-minimum potential well along the coordinate of proton motion. The weight losses due to thermal decomposition of L-and D-tartaric acid were observed to occur at 443.0 and 443.2 K, respectively, and at 306.1 and 480.6 K for MDL-tartaric acid. The weight losses for L-and D-tartaric acid during decomposition were probably caused by the evolution of 3H 2 O and 3CO gases. By considering proton transfer between two possible sites in the hydrogen bond, we concluded that the weight losses at 306.1 and 480.6 K for MDL-tartaric acid were caused by the evaporation of half the bound water molecules in the sample, and by the evaporation of the remaining water molecules and the evolution of 3H 2 O and 3CO gases, respectively.
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