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H. Takayama

Publications and source records attributed to H. Takayama.

16 recordsLinked to original sources
arXiv2007

Scaling Analysis of Domain-Wall Free-Energy in the Edwards-Anderson Ising Spin Glass in a Magnetic Field

The stability of the spin-glass phase against a magnetic field is studied in the three and four dimensional Edwards-Anderson Ising spin glasses. Effective couplings and effective fields associated with length scale L are measured by a numerical domain-wall renormalization group method. The results obtained by scaling analysis of the data strongly indicate the existence of a crossover length beyond which the spin-glass order is destroyed by field H. The crossover length well obeys a power law of H which diverges as H goes to zero but remains finite for any non-zero H, implying that the spin-glass phase is absent even in an infinitesimal field. These results are well consistent with the droplet theory for short-range spin glasses.

cond-mat.dis-nn↗
arXiv2007

Extended Scaling for Ferromagnets

A simple systematic rule, inspired by high-temperature series expansion (HTSE) results, is proposed for optimizing the expression for thermodynamic observables of ferromagnets exhibiting critical behavior at $\Tc$. This ``extended scaling'' scheme leads to a protocol for the choice of scaling variables, $τ=(T-\Tc)/T$ or $(T^2 - \Tc^2)/T^2$ depending on the observable instead of $(T-\Tc)/\Tc$, and more importantly to temperature dependent non-critical prefactors for each observable. The rule corresponds to scaling of the leading of the reduced susceptibility above $\Tc$ as $χ_{\rm c}^{*}(T)\sim τ^{-γ}$ in agreement with standard practice with scaling variable $τ$, and for the leading term of the second-moment correlation length as $ξ_{\rm c}^{*}(T)\sim T^{-1/2}τ^{-ν}$. For the specific heat in bipartite lattices the rule gives $C_{\rm c}^{*}(T) \sim T^{-2}[(T^2 -\Tc^2)/T^2]^{-α}$. The latter two expressions are not standard. The scheme can allow for confluent and non-critical correction terms. A stringent test of the extended scaling is made through analyses of high precision numerical and HTSE data, or {\it real} data, on the three-dimensional canonical Ising, XY, and Heisenberg ferromagnets.

cond-mat.stat-mech↗
arXiv2006

An Extended Scaling Scheme for Critically Divergent Quantities in Ferromagnets and Spin Glasses

From a consideration of high temperature series expansions in ferromagnets and in spin glasses, we propose an extended scaling scaling scheme involving a set of scaling formulae which express 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 binomial Ising spin glass, leads to consistency for the estimates of critical parameters obtained from scaling analyses for different observables.

cond-mat.stat-mech↗
arXiv2005

Temperature Chaos and Bond Chaos in the Edwards-Anderson Ising Spin Glass : Domain-Wall Free-Energy Measurements

Domain-wall free-energy $δF$, entropy $δS$, and the correlation function, $C_{\rm temp}$, of $δF$ are measured independently in the four-dimensional $\pm J$ Edwards-Anderson (EA) Ising spin glass. The stiffness exponent $θ$, the fractal dimension of domain walls $d_{\rm s}$ and the chaos exponent $ζ$ are extracted from the finite-size scaling analysis of $δF$, $δS$ and $C_{\rm temp}$ respectively well inside the spin-glass phase. The three exponents are confirmed to satisfy the scaling relation $ζ=d_{\rm s}/2-θ$ derived by the droplet theory within our numerical accuracy. We also study bond chaos induced by random variation of bonds, and find that the bond and temperature perturbations yield the universal chaos effects described by a common scaling function and the chaos exponent. These results strongly support the appropriateness of the droplet theory for the description of chaos effect in the EA Ising spin glasses.

cond-mat.dis-nn↗
arXiv2005

Neel Temperature of Quasi-Low-Dimensional Heisenberg Antiferromagnets

The Néel temperature, $T_{\rm N}$, 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 (inter-layer) to intra-chain (intra-layer) coupling $J'/J$ down to $J'/J\simeq 10^{-3}$. We find that $T_{\rm N}$ 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 $T_{\rm N}$ for a wide range of $J'$ and useful for the analysis of experimental measurements are presented.

cond-mat.str-el↗
arXiv2005

Dynamical breakdown of the Ising spin-glass order under a magnetic field

The dynamical magnetic properties of an Ising spin glass Fe$_{0.55}$Mn$_{0.45}$TiO$_3$ are studied under various magnetic fields. Having determined the temperature and static field dependent relaxation time $τ(T;H)$ from ac magnetization measurements under a dc bias field by a general method, we first demonstrate that these data provide evidence for a spin-glass (SG) phase transition only in zero field. We next argue that the data $τ(T;H)$ of finite $H$ can be well interpreted by the droplet theory which predicts the absence of a SG phase transition in finite fields.

cond-mat.dis-nn↗
arXiv2004

Aging and Memory Effects in Superparamagnets and Superspin Glasses

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.

cond-mat.dis-nn↗
arXiv2004

Absence of rejuvenation in a Superspin Glass

Effects of temperature changes on the nonequilibrium spin-glass dynamics of a strongly interacting ferromagnetic nanoparticle system (superspin glass) are studied. In contrary to atomic spin glasses, strong cooling rate effects are observed, and no evidence for temperature-chaos is found. The flip time of a magnetic moment is much longer than that of an atomic spin and hence much shorter time scales are probed within the experimental time window for a superspin glass than for an atomic spin glass. Within a real space picture the cumulative aging observed for the superspin glass can be explained considering that all investigated length scales are shorter than the temperature-chaos overlap length. The transient relaxation, observed in experiments after temperature changes, can be understood as the adjustment of thermally active droplets, which is mutatis mutandis the Kovacs effect observed in most glassy systems.

cond-mat.dis-nn↗
arXiv2004

Comment on "Memory Effects in an Interacting Magnetic Nanoparticle System"

In Phys. Rev. Lett. 91 167206 (2003), Sun et al. study memory effects in an interacting nanoparticle system with specific temperature and field protocols. The authors claim that the observed memory effects originate from spin-glass dynamics and that the results are consistent with the hierarchical picture of the spin-glass phase. In this comment, we argue their claims premature by demonstrating that all their experimental curves can be reproduced qualitatively using only a simplified model of isolated nanoparticles with a temperature dependent distribution of relaxation times.

cond-mat.dis-nn↗
arXiv2003

Aging phenomena in spin glasses: theory, experiment, and simulation

We study numerically temperature-shift and field-shift aging protocols on the 3-dimensional (3D) Ising Edwards-Anderson (EA) spin-glass (SG) model focusing on respectively the temperature-chaos nature and the stability under a static field of the SG phase. The results of the latter strongly support the droplet theory which predicts the instability of the SG phase under the field. They are also discussed in relation with the experimental studies.

cond-mat.dis-nn↗
arXiv2000

Classical Correlation-Length Exponent in Non-Universal Quantum Phase Transition of Diluted Heisenberg Antiferromagnet

Critical behavior of the quantum phase transition of a site-diluted Heisenberg antiferromagnet on a square lattice is investigated by means of the quantum Monte Carlo simulation with the continuous-imaginary-time loop algorithm. Although the staggered spin correlation function decays in a power law with the exponent definitely depending on the spin size $S$, the correlation-length exponent is classical, i.e., $ν=4/3$. This implies that the length scale characterizing the non-universal quantum phase transition is nothing but the mean size of connected spin clusters.

cond-mat.dis-nn↗
arXiv1999

Numerical Study on Aging Dynamics in the 3D Ising Spin-Glass Model --- Quasi-Equilibrium Behaviour of Spin Auto-Correlation Functions

Using Monte Carlo simulations, we have studied aging phenomena in three-dimensional Gaussian Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation functions. Weak violation of the time translational invariance in the quasi-equilibrium regime is analyzed in terms of effective stiffness for droplet excitations in the presence of domain walls. The simulated results in not only isothermal but also $T$-shift aging processes exhibit the expected scaling behavior with respect to the characteristic length scales associated with droplet excitations and domain walls in spite of the fact that the growth law for these length scales still shows a pre-asymptotic behavior compared with the asymptotic form proposed by the droplet theory. Implications of our simulational results are also discussed in relation to experimental observations.

cond-mat.dis-nn↗
arXiv1999

Quantum Phase Transition of Randomly-Diluted Heisenberg Antiferromagnet on a Square Lattice

Ground-state magnetic properties of the diluted Heisenberg antiferromagnet on a square lattice are investigated by means of the quantum Monte Carlo method with the continuous-time loop algorithm. It is found that the critical concentration of magnetic sites is independent of the spin size S, and equal to the two-dimensional percolation threshold. However, the existence of quantum fluctuations makes the critical exponents deviate from those of the classical percolation transition. Furthermore, we found that the transition is not universal, i.e., the critical exponents significantly depend on S.

cond-mat.dis-nn↗
arXiv1998

Fully Frustrated Ising System on a 3D Simple Cubic Lattice: Revisited

Using extensive Monte Carlo simulations, we clarify the critical behaviour of the 3 dimensional simple cubic Ising Fully Frustrated system. We find two transition temperatures and two long range ordered phases. Within the present numerical accuracy, the transition at higher temperature is found to be second order and we have extracted the standard critical exponent using finite size scaling method. On the other hand, the transition at lower temperature is found to be first order. It is argued that entropy plays a major role on determining the low temperature state.

cond-mat.stat-mech↗
arXiv1997

Mean-field theory for a spin-glass model of neural networks: TAP free energy and paramagnetic to spin-glass transition

An approach is proposed to the Hopfield model where the mean-field treatment is made for a given set of stored patterns (sample) and then the statistical average over samples is taken. This corresponds to the approach made by Thouless, Anderson and Palmer (TAP) to the infinite-range model of spin glasses. Taking into account the fact that in the Hopfield model there exist correlations between different elements of the interaction matrix, we obtain its TAP free energy explicitly, which consists of a series of terms exhibiting the cluster effect. Nature of the spin-glass transition in the model is also examined and compared with those given by the replica method as well as the cavity method.

cond-mat.dis-nn↗