arXiv subjects

Kazutaka Takahashi

Publications and source records attributed to Kazutaka Takahashi.

51 records · Page 3Linked to original sources

arXiv2011

Ensemble Inequivalence and the Spin-Glass Transition

We report on the ensemble inequivalence in a many-body spin-glass model with integer spin. The spin-glass phase transition is of first order for certain values of the crystal field strength and is dependent whether it was derived in the microcanonical or the canonical ensemble. In the limit of infinitely many-body interactions, the model is the integer-spin equivalent of the random-energy model, and is solved exactly. We also derive the integer-spin equivalent of the de Almeida-Thouless line.

cond-mat.dis-nn↗

arXiv2011

Ensemble equivalence in spin systems with short-range interactions

We study the problem of ensemble equivalence in spin systems with short-range interactions under the existence of a first-order phase transition. The spherical model with nonlinear nearest-neighbour interactions is solved exactly both for canonical and microcanonical ensembles. The result reveals apparent ensemble inequivalence at the first-order transition point in the sense that the microcanonical entropy is non-concave as a function of the energy and consequently the specific heat is negative. In order to resolve the paradox, we show that an unconventional saddle point should be chosen in the microcanonical calculation that represents a phase separation. The XY model with non-linear interactions is also studied by microcanonical Monte Carlo simulations in two dimensions to see how this model behaves in comparison with the spherical model.

cond-mat.stat-mech↗

arXiv2011

Replica analysis of partition-function zeros in spin-glass models

We study the partition-function zeros in mean-field spin-glass models. We show that the replica method is useful to find the locations of zeros in a complex parameter plane. For the random energy model, we obtain the phase diagram in the plane and find that there are two types of distribution of zeros: two-dimensional distribution within a phase and one-dimensional one on a phase boundary. Phases with a two-dimensional distribution are characterized by a novel order parameter defined in the present replica analysis. We also discuss possible patterns of distributions by studying several systems.

cond-mat.dis-nn↗

arXiv2011

Statistical mechanical analysis of a hierarchical random code ensemble in signal processing

We study a random code ensemble with a hierarchical structure, which is closely related to the generalized random energy model with discrete energy values. Based on this correspondence, we analyze the hierarchical random code ensemble by using the replica method in two situations: lossy data compression and channel coding. For both the situations, the exponents of large deviation analysis characterizing the performance of the ensemble, the distortion rate of lossy data compression and the error exponent of channel coding in Gallager's formalism, are accessible by a generating function of the generalized random energy model. We discuss that the transitions of those exponents observed in the preceding work can be interpreted as phase transitions with respect to the replica number. We also show that the replica symmetry breaking plays an essential role in these transitions.

cond-mat.dis-nn↗

arXiv2010

Replica symmetry breaking, complexity and spin representation in the generalized random energy model

We study the random energy model with a hierarchical structure known as the generalized random energy model (GREM). In contrast to the original analysis by the microcanonical ensemble formalism, we investigate the GREM by the canonical ensemble formalism in conjunction with the replica method. In this analysis, spin-glass-order parameters are defined for respective hierarchy level, and all possible patterns of replica symmetry breaking (RSB) are taken into account. As a result, we find that the higher step RSB ansatz is useful for describing spin-glass phases in this system. For investigating the nature of the higher step RSB, we generalize the notion of complexity developed for the one-step RSB to the higher step and demonstrate how the GREM is characterized by the generalized complexity. In addition, we propose a novel mean-field spin-glass model with a hierarchical structure, which is equivalent to the GREM at a certain limit. We also show that the same hierarchical structure can be implemented to other mean-field spin models than the GREM. Such models with hierarchy exhibit phase transitions of multiple steps in common.

cond-mat.dis-nn↗

arXiv2010

Energy-gap analysis of quantum spin-glass transitions at zero temperature

We study for random quantum spin systems the energy gap between the ground and first excited states to clarify a relation to the spin-glass-paramagnetic phase transition. We find that for the transverse Sherrington-Kirkpatrick model the vanishing of the averaged gap does not identify the transition. A power-law form of the gap distribution function leads to power-law distributions of the linear, spin-glass, and nonlinear susceptibilities. They diverge at different points, which we attribute to a quantum Griffiths mechanism. On the other hand, the classical treatment is justified for the transverse random energy model and the phase transition can be found by a sudden change of the ground state.

cond-mat.dis-nn↗

arXiv2010

Effect of random fluctuations on quantum spin-glass transitions at zero temperature

We study the effects of random fluctuations on quantum phase transitions by the energy gap analysis. For the infinite-ranged spin-glass models with a transverse field, we find that a strong sample-to-sample fluctuation effect leads to broad distributions of the energy gap. As a result, the linear, spin-glass, and nonlinear susceptibilities behave differently from each other. The power-law tail of the distribution implies a quantum Griffiths-like effect that could be observed in various random quantum systems. We also discuss the mechanisms of the phase transition in terms of the energy gap by comparing the Sherrington-Kirkpatrick model and random energy model, which demonstrate the difference between the continuous and discontinuous phase transitions.

cond-mat.dis-nn↗

arXiv2008

Dynamical correlations in the Sherrington-Kirkpatrick model in a transverse field

We calculate the real-time-correlation function of the Sherrington-Kirkpatrick spin-glass model in a transverse field. Using a careful analysis of the perturbative expansion of the functional-integral representation, we derive the asymptotic form of the correlation function. In contrast to the previous works, we find for large transverse field a power-law decay of the correlation with time $t$ as $t^{-3/2}$ at zero temperature and $t^{-2}$ at infinite temperature. At the small field region, we also find a significant change in the correlation which comes from the structural difference between two paramagnetic phases.

cond-mat.dis-nn↗

arXiv2007

Quantum fluctuations in the transverse Ising spin glass model: A field theory of random quantum spin systems

We develop a mean-field theory for random quantum spin systems using the spin coherent state path integral representation. After the model is reduced to the mean field one-body Hamiltonian, the integral is analyzed with the aid of several methods such as the semiclassical method and the gauge transformation. As an application we consider the Sherrington-Kirkpatrick model in a transverse field. Using the Landau expansion and its improved versions, we give a detailed analysis of the imaginary-time dependence of the order parameters. Integrating out the quantum part of the order parameters, we obtain the effective renormalized free energy written in terms of the classically defined order parameters. Our method allows us to obtain the spin glass-paramagnetic phase transition point $Γ/J\sim 1.62$ at T=0.

cond-mat.dis-nn↗

arXiv2007

Chaotic scattering through coupled cavities

We study the chaotic scattering through an Aharonov-Bohm ring containing two cavities. One of the cavities has well-separated resonant levels while the other is chaotic, and is treated by random matrix theory. The conductance through the ring is calculated analytically using the supersymmetry method and the quantum fluctuation effects are numerically investigated in detail. We find that the conductance is determined by the competition between the mean and fluctuation parts. The dephasing effect acts on the fluctuation part only. The Breit-Wigner resonant peak is changed to an antiresonance by increasing the ratio of the level broadening to the mean level spacing of the random cavity, and the asymmetric Fano form turns into a symmetric one. For the orthogonal and symplectic ensembles, the period of the Aharonov-Bohm oscillations is half of that for regular systems. The conductance distribution function becomes independent of the ensembles at the resonant point, which can be understood by the mode-locking mechanism. We also discuss the relation of our results to the random walk problem.

cond-mat.mes-hall↗

arXiv2006

Mesoscopic conductance fluctuations in a coupled quantum dot system

We study the transport properties of an Aharonov-Bohm ring containing two quantum dots. One of the dots has well-separated resonant levels, while the other is chaotic and is treated by random matrix theory. We find that the conductance through the ring is significantly affected by mesoscopic fluctuations. The Breit-Wigner resonant peak is changed to an antiresonance by increasing the ratio of the level broadening to the mean level spacing of the random dot. The asymmetric Fano form turns into a symmetric one and the resonant peak can be controlled by magnetic flux. The conductance distribution function clearly shows the influence of strong fluctuations.

cond-mat.mes-hall↗

arXiv2004

Nonlinear sigma model approach for level correlations in chiral disordered systems

We study level correlations of disordered systems with chiral unitary symmetry (AIII symmetry). We use a random matrix model with a finite correlation length to derive a supersymmetric nonlinear sigma model. The result is compared with existing results based on other models. Using the methods by Kravtsov and Mirlin (Pis'ma Zh. Eksp. Teor. Fiz. 60, 645 (1994) [JETP Lett. 60, 656 (1994)]) and Andreev and Altshuler [Phys. Rev. Lett. 75, 902 (1995)], we calculate the density of states and two-level correlation function. The result is expressed using the spectral determinant as in traditional nonchiral systems. We discuss the renormalization of the mean level spacing which is not present in the traditional systems.

cond-mat.dis-nn↗

arXiv2004

Long range disorder and Anderson transition in systems with chiral symmetry

We study the spectral properties of a chiral random banded matrix (chRBM) with elements decaying as a power-law ${{\cal H}_{ij}}\sim |i-j|^{-α}$. This model is equivalent to a chiral 1D Anderson Hamiltonian with long range power-law hopping. In the weak disorder limit we obtain explicit nonperturbative analytical results for the density of states and the two-level correlation function by mapping the chRBM onto a nonlinear sigma model. We also put forward, by exploiting the relation between the chRBM at $α=1$ and a generalized chiral random matrix model, an exact expression for the above correlation functions. We give compelling analytical and numerical evidence that for this value the chRBM reproduces all the features of an Anderson transition. Finally we discuss possible applications of our results to QCD.

cond-mat.dis-nn↗

arXiv2002

Effect of spin on electron motion in a random magnetic field

We consider properties of a two-dimensional electron system in a random magnetic field. It is assumed that the magnetic field not only influences orbital electron motion but also acts on the electron spin. For calculations, we suggest a new trick replacing the initial Hamiltonian by a Dirac Hamiltonian. This allows us to do easily a perturbation theory and derive a supermatrix sigma model, which takes a form of the conventional sigma model with the unitary symmetry. Using this sigma model we calculate several correlation functions including a spin-spin correlation function. As compared to the model without spin, we get different expressions for the single-particle lifetime and the transport time. The diffusion constant turns out to be 2 times smaller than the one for spinless particles.

cond-mat.mes-hall↗

arXiv2001

Energy-level correlations in chiral symmetric disordered systems: Corrections to the universal results

We investigate the deviation of the level-correlation functions from the universal form for the chiral symmetric classes. Using the supersymmetric nonlinear sigma model we formulate the perturbation theory. The large energy behavior is compared with the result of the diagrammatic perturbation theory. We have the diffuson and cooperon contributions even in the average density of states. For the unitary and orthogonal classes we get the small energy behavior that suggests a weakening of the level repulsion. For the symplectic case we get a result with opposite tendency.

cond-mat.dis-nn↗