Many dense magnetic nanoparticle systems exhibit slow dynamics which is qualitatively indistinguishable from that observed in atomic spin glasses and its origin is attributed to dipole interactions among particle moments (or superspins). However, even in dilute nanoparticle systems where the dipole interactions are vanishingly small, slow dynamics is observed and is attributed solely to a broad distribution of relaxation times which in turn comes from that of the anisotropy energy barriers. To clarify characteristic differences between the two types of slow dynamics, we study a simple model of a non-interacting nanoparticle system (a superparamagnet) analytically as well as ferritin (a superparamagnet) and a dense Fe-N nanoparticle system (a superspin glass) experimentally. It is found that superparamagnets in fact show aging (a waiting time dependence) of the thermoremanent-magnetization as well as various memory effects. We also find some dynamical phenomena peculiar only to superspin glasses such as the flatness of the field-cooled magnetization below the critical temperature and memory effects in the zero-field-cooled magnetization. These dynamical phenomena are qualitatively reproduced by the random energy model, and are well interpreted by the so-called droplet theory in the field of the spin-glass study.

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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.

From a consideration of high temperature series expansions in ferromagnets and in spin glasses, we propose an extended scaling scheme involving a set of scaling formulas which expresses to leading order the temperature (T) and the system size (L) dependences of thermodynamic observables over a much wider range of T than the corresponding one in the conventional scaling scheme. The extended scaling, illustrated by data on the canonical 2d ferromagnet and on the 3d bimodal Ising spin glass, leads to consistency in the estimates of critical parameters obtained from scaling analyses for different observables.