Retrieval Properties of Hopfield and Correlated Attractors in an Associative Memory Model

We examine a previouly introduced attractor neural network model that explains the persistent activities of neurons in the anterior ventral temporal cortex of the brain. In this model, the coexistence of several attractors including correlated attractors was reported in the cases of finite and infinite loading. In this paper, by means of a statistical mechanical method, we study the statics and dynamics of the model in both finite and extensive loading, mainly focusing on the retrieval properties of the Hopfield and correlated attractors. In the extensive loading case, we derive the evolution equations by the dynamical replica theory. We found several characteristic temporal behaviours, both in the finite and extensive loading cases. The theoretical results were confirmed by numerical simulations.Comment: 12 pages, 7 figure

Successive phase transitions at finite temperatures of the supersolid in the three-dimensional extended Bose-Hubbard model

We study the finite temperature properties of the extended Bose-Hubbard model on a cubic lattice. This model exhibits the so-called supersolid state. To start with, we investigate ordering processes by quantum Monte Carlo simulations, and find successive superfluid and solid phase transitions. There, we find that the two order parameters compete with each other. We obtain the finite temperature phase diagram, which contains the superfluid, the solid, the supersolid and the disordered phase. We develop a mean-field theory to analyze the ordering processes and compare the result with that obtained by simulations, and discuss the mechanism of the competition of these two orders. We also study how the supersolid region shrinks as the on-site repulsion becomes strong.Comment: 6 pages, 6 figure

Slow Relaxation Process in Ising like Heisenberg Kagome Antiferromagnets due to Macroscopic Degeneracy in the Ordered State

We study relaxation phenomena in the ferromagnetically ordered state of the Ising-like Heisenberg kagome antiferromagnets. We introduce the "weathervane loop" in order to characterize macroscopic degenerate ordered states and study the microscopic mechanism of the slow relaxation from a view point of the dynamics of the weathervane loop configuration. This mechanism may give a possible origin of the slow relaxation reported in recent experiments.Comment: 6pages, 4figures, HFM2006 proceeding

Quantum Decoherence at Finite Temperatures

We study measures of decoherence and thermalization of a quantum system $S$ in the presence of a quantum environment (bath) $E$. The whole system is prepared in a canonical thermal state at a finite temperature. Applying perturbation theory with respect to the system-environment coupling strength, we find that under common Hamiltonian symmetries, up to first order in the coupling strength it is sufficient to consider the uncoupled system to predict decoherence and thermalization measures of $S$. This decoupling allows closed form expressions for perturbative expansions for the measures of decoherence and thermalization in terms of the free energies of $S$ and of $E$. Numerical results for both coupled and decoupled systems with up to 40 quantum spins validate these findings.Comment: 5 pages, 3 figure

Feedback Effect on Landau-Zener-Stueckelberg Transitions in Magnetic Systems

We examine the effect of the dynamics of the internal magnetic field on the staircase magnetization curves observed in large-spin molecular magnets. We show that the size of the magnetization steps depends sensitively on the intermolecular interactions, even if these are very small compared to the intra-molecular couplings.Comment: 4 pages, 3 Postscript figures; paper reorganized, conclusions modifie

Structure of Metastable States in Phase Transitions with High-Spin Low-Spin Degree of Freedom

Difference of degeneracy of the low-spin (LS) and high-spin (HS) states causes interesting entropy effects on spin-crossover phase transitions and charge transfer phase transitions in materials composed of the spin-crossover atoms. Mechanisms of the spin-crossover (SC) phase transitions have been studied by using Wajnflasz model, where the degeneracy of the spin states (HS or LS) is taken into account and cooperative natures of the spin-crossover phase transitions have been well described. Recently, a charge transfer (CT) phase transition due to electron hopping between LS and HS sites has been studied by using a generalized Wajnflasz model. In the both systems of SC and CT, the systems have a high temperature structure (HT) and a low temperature structure (LT), and the change between them can be a smooth crossover or a discontinuous first order phase transition depending on the parameters of the systems. Although apparently the standard SC system and the CT system are very different, it is shown that both models are equivalent under a certain transformation of variables. In both systems, the structure of metastable state at low temperatures is a matter of interest. We study temperature dependence of fraction of HT systematically in a unified model, and find several structures of equilibrium and metastable states of the model as functions of system parameters. In particular, we find a reentrant type metastable branch of HT in a low temperature region, which would play an important role to study the photo-irradiated processes of related materials.Comment: 19 pages, 11 figure

Effect of a Spin-1/2 Impurity on the Spin-1 Antiferromagnetic Heisenberg Chain

Low-lying excited states as well as the ground state of the spin-1 antiferro- magnetic Heisenberg chain with a spin-1/2 impurity are investigated by means of a variational method and a method of numerical diagonalization. It is shown that 1) the impurity spin brings about massive modes in the Haldane gap, 2) when the the impurity-host coupling is sufficiently weak, the phenomenological Hamiltonian used by Hagiwara {\it et al.} in the analysis of ESR experimental results for NENP containing a small amount of spin-1/2 Cu impurities is equivalent to a more realistic Hamiltonian, as far as the energies of the low-lying states are concerned, 3) the results obtained by the variational method are in semi-quantitatively good agreement with those obtained by the numerical diagonalization.Comment: 11 pages, plain TeX (Postscript figures are included), KU-CCS-93-00

Ordered phase and phase transitions in the three-dimensional generalized six-state clock model

We study the three-dimensional generalized six-state clock model at values of the energy parameters, at which the system is considered to have the same behavior as the stacked triangular antiferromagnetic Ising model and the three-state antiferromagnetic Potts model. First, we investigate ordered phases by using the Monte Carlo twist method (MCTM). We confirmed the existence of an incompletely ordered phase (IOP1) at intermediate temperature, besides the completely ordered phase (COP) at low-temperature. In this intermediate phase, two neighboring states of the six-state model mix, while one of them is selected in the low temperature phase. We examine the fluctuation the mixing rate of the two states in IOP1 and clarify that the mixing rate is very stable around 1:1. The high temperature phase transition is investigated by using non-equilibrium relaxation method (NERM). We estimate the critical exponents beta=0.34(1) and nu=0.66(4). These values are consistent with the 3D-XY universality class. The low temperature phase transition is found to be of first-order by using MCTM and the finite-size-scaling analysis

Fluctuations and vortex pattern ordering in fully frustrated XY model with honeycomb lattice

The accidental degeneracy of various ground states in a fully frustrated XY model with a honeycomb lattice is shown to survive even when the free energy of the harmonic fluctuations is taken into account. The reason for that consists in the existence of a hidden gauge symmetry between the Hamiltonians describing the harmonic fluctuations in all these ground states. A particular vortex pattern is selected only when anharmonic fluctuations are taken into account. However, the observation of vortex ordering requires relatively large system size L>>100000.Comment: 4 pages, 2 figures, RevTeX4, a different method is used to find which state is selected by anharmonic fluctuations, the last third of the text is completly rewritte

Spin-Peierls transition of the first order in S=1 antiferromagnetic Heisenberg chains

We investigate a one-dimensional S=1 antiferromagnetic Heisenberg model coupled to a lattice distortion by a quantum Monte Carlo method. Investigating the ground state energy of the static bond-alternating chain, we find that the instability to a dimerized chain depends on the value of the spin-phonon coupling, unlike the case of S=1/2. The spin state is the dimer state or the uniform Haldane state depending on whether the lattice distorts or not, respectively. At an intermediate value of the spin-phonon coupling, we find the first-order transition between the two states. We also find the coexistence of the two states.Comment: 7 pages, 12 eps figures embedded in the text; corrected typos, replaced figure