arXiv subjects

Chiaki Yamaguchi

Publications and source records attributed to Chiaki Yamaguchi.

17 recordsLinked to original sources

arXiv2019

Proposal of a new quantum annealing schedule for studying quantum annealing of transverse field Ising models

Recently, Heim, Ronnow, Isakov and Troyer [Science 348 (2015) 215] have reported that Monte Carlo simulations for the Ising spin glass model on the square lattice in the physically relevant continuous-imaginary-time limit do not show superiority of quantum annealing (QA) using transverse field against classical annealing (CA). Although the QA schedule that they had used has been using conventionally, however the QA schedule mathematically has no guarantee that the used schedule is the best QA schedule for performance of optimization. We propose a new QA schedule for studying transverse-field-based quantum versus classical annealing of the Ising model. The present QA schedule utilizes a smallest effective transverse field derived in this article. This QA schedule is made for the comparison between the system with no transverse field and the system with the smallest effective transverse field. As a case study, we study QA of the Ising spin glass model on the square lattice at low but finite temperature. A Monte Carlo algorithm using the physically relevant continuous-imaginary-time limit is performed. As the simulation results, we show superiority of QA against CA when the annealing time is sufficiently spent.

cond-mat.dis-nn↗

arXiv2015

Proposal of a Checking Parameter in the Simulated Annealing Method Applied to the Spin Glass Model

We propose a checking parameter utilizing the breaking of the Jarzynski equality in the simulated annealing method using the Monte Carlo method. This parameter is based on the Jarzynski equality. By using this parameter, to detect that the system is in global minima of the free energy under gradual temperature reduction is possible. Thus, by using this parameter, one is able to investigate the efficiency of annealing schedules. We apply this parameter to the +-J Ising spin glass model. The application to the Gaussian Ising spin glass model is also mentioned. We discuss that the breaking of the Jarzynski equality is induced by the system being trapped in local minima of the free energy. By performing Monte Carlo simulations of the +-J Ising spin glass model and a glassy spin model proposed by Newman and Moore, we show the efficiency of the use of this parameter.

cond-mat.dis-nn↗

arXiv2015

A curious relationship between Potts glass models

A Potts glass model proposed by Nishimori and Stephen[H. Nishimori and M. J. Stephen, Phys. Rev. B 27, 5644 (1983)] is analyzed by means of the replica mean field theory. This model is a discrete model, has a gauge symmetry, and is called the Potts gauge glass model. By comparing the present results with the results of the conventional Potts glass model, we find the coincidences and differences between the models. We find a coincidence that the property for the Potts glass phase in this model is coincident with that in the conventional model at the mean field level. We find a difference that, unlike in the case of the conventional $p$-state Potts glass model, this system for large $p$ does not become ferromagnetic at low temperature under a concentration of ferromagnetic interaction. The present results support the act of numerically investigating the present model for study of the Potts glass phase in finite dimensions.

cond-mat.dis-nn↗

arXiv2014

Analytical estimates of the locations of phase transition points in the ground state for the bimodal Ising spin glass model in two dimensions

We analytically estimate the locations of phase transition points in the ground state for the $\pm J$ random bond Ising model with asymmetric bond distributions on the square lattice. We propose and study the percolation transitions for two types of bond shared by two non-frustrated plaquettes. The present method indirectly treats the sizes of clusters of correlated spins for the ferromagnetic and spin glass orders. We find two transition points. The first transition point is the phase transition point for the ferromagnetic order, and the location is obtained as $p_c^{(1)} \approx 0.895 \, 399 \, 54$ as the solution of $[p^2 + 3 (1-p)^2 ]^2 \, p^3 - \frac{1}{2} = 0$. The second transition point is the phase transition point for the spin glass order, and the location is obtained as $p_c^{(2)} = \frac{1}{4} [2 + \sqrt{2 (\sqrt{5} - 1)}] \approx 0.893 \, 075 \, 69$. Here, $p$ is the ferromagnetic bond concentration, and $1 - p$ is the antiferromagnetic bond concentration. The obtained locations are reasonably close to the previously estimated locations. This study suggests the presence of the intermediate phase between $p_c^{(1)}$ and $p_c^{(2)}$; however, since the present method produces remarkable values but has no mathematical proof for accuracy yet, no conclusions are drawn in this article about the presence of the intermediate phase.

cond-mat.dis-nn↗

arXiv2013

Conjectured Exact Percolation Thresholds of the Fortuin-Kasteleyn Cluster for the +-J Ising Spin Glass Model

The conjectured exact percolation thresholds of the Fortuin-Kasteleyn cluster for the +-J Ising spin glass model are theoretically shown based on a conjecture. It is pointed out that the percolation transition of the Fortuin-Kasteleyn cluster for the spin glass model is related to a dynamical transition for the freezing of spins. The present results are obtained as locations of points on the so-called Nishimori line, which is a special line in the phase diagram. We obtain TFK = 2 / ln [z / (z - 2)] and pFK = z / [2 (z - 1)] for the Bethe lattice, TFK -> infinity and pFK -> 1 / 2 for the infinite-range model, TFK = 2 / ln 3 and pFK = 3 / 4 for the square lattice, TFK ~ 3.9347 and pFK ~ 0.62441 for the simple cubic lattice, TFK ~ 6.191 and pFK ~ 0.5801 for the 4-dimensional hypercubic lattice, and TFK = 2 / ln {[1 + 2 sin (pi / 18)] / [1 - 2 sin (pi / 18) ]} and pFK = [1 + 2 sin (pi / 18) ] / 2 for the triangular lattice, when J / kB = 1, where z is the coordination number, J is the strength of the exchange interaction between spins, kB is the Boltzmann constant, TFK is the temperature at the percolation transition point, and pFK is the probability, that the interaction is ferromagnetic, at the percolation transition point.

cond-mat.dis-nn↗

arXiv2012

Analysis of an Extended +-J Ising Spin Glass Model by Using a Gauge Symmetry

We investigate an extended +-J Ising spin glass model by using a gauge symmetry. This model has +-J1 interactions and +-J2 interactions. We show that a gauge symmetry is usable to study this model. The exact internal energy, the rigorous upper bound of the specific heat and some rigorous relations for correlation functions and order parameters are shown by using the gauge symmetry. The results are rigorous, and do not depend on any lattice shape. A part of our results, e.g., the value of the exact internal energy should be useful for checking the computer programs for investigating this model. In addition, we find that the present solutions are general solutions which include the solutions on the so-called Nishimori line for the conventional +-J Ising spin glass model and the solutions for the bond-diluted +-J Ising spin glass model.

cond-mat.dis-nn↗

arXiv2012

Static Exact Solutions of a Spin Model Exhibiting Glassy Dynamics

A spin model which exhibits glassy dynamics has been proposed by Newman and Moore. This model possesses no randomness for exchange interactions. We propose partial trace methods for obtaining static exact solutions of this model under free boundary conditions, and show some static exact solutions. We obtain that, from the exact solutions of the specific heat and the correlation functions, the transition temperature is zero, although the thermal average of a spin is zero when the temperature is zero. We investigate the ground states. In the ground states, a part of the present results especially disagrees with the part of the previous results. We discuss the disagreements.

cond-mat.stat-mech↗

arXiv2012

Exact Results for the Jarzynski Equality in Ising Spin Glass Models Derived by Using a Gauge Symmetry

Exact results for the Jarzynski equality are derived for Ising spin glass models. The Jarzynski equality is an equality that connects the work in nonequilibrium and the difference between free energies. The work is performed in switching an external parameter of the system. As the Ising spin glass models, the +-J model and the Gaussian model are investigated. For the +-J model and the Gaussian model, we derive exact lower bounds of the exponentiated work for investigating the ferromagnetic phases and the multicritical points, and derive rigorous relations between the exponentiated work which have different quenched random configurations. For the Gaussian model, we derive the exact exponentiated work for investigating the spin glass phase. Exact results for the infinite-range models are also obtained. The present results are obtained by using a gauge symmetry, and are related to points on the Nishimori lines which are special lines in the phase diagrams. The present results do not depend on any lattice shape, and a part of the present results instead depends on the number of nearest-neighbor pairs in the whole system.

cond-mat.dis-nn↗

arXiv2012

The Derivation of the Exact Internal Energies for Spin Glass Models by Applying the Gauge Theory to the Fortuin-Kasteleyn Representation

We derive the exact internal energies and the rigorous upper bounds of specific heats for several spin glass models by applying the gauge theory to the Fortuin-Kasteleyn representation which is a representation based on a percolation picture for spin-spin correlation. The results are derived on the Nishimori lines which are special lines on the phase diagrams. As the spin glass models, the +-J Ising model and a Potts gauge glass model are studied. The present solutions agree with the previous solutions. The derivation of the solutions by the present method must be useful for understanding the relationship between the percolation picture for spin-spin correlation and the physical quantities on the Nishimori line.

cond-mat.dis-nn↗

arXiv2011

An analytical application of Niedermayer's algorithm to the Edwards-Anderson model: analytical results for the multicritical point on the Nishimori line

We apply analytically Niedermayer's algorithm to the Edwards-Anderson model on random graphs with arbitary degree distributions. The results for the multicritical point on the Nishimori line are shown. The results are shown by applying a criterion for spin models on the random graphs with arbitary degree distributions. The application of Niedermayer's algorithm makes the size of the Fortuin-Kasteleyn cluster small and shifts the percolation threshold. The results for the $\pm J$ model and the Gaussian model are respectively shown. In the present article, it is respectively shown for the $\pm J$ model and the Gaussian model that, by adjusting an introduced parameter for Niedermayer's algorithm, the percolation threshold obtained in the present article agrees with the location of the multicritical point. We naively estimate the locations of the multicritical points for the $\pm J$ model and the Gaussian model on the randam graphs with arbitary degree distributions.

cond-mat.dis-nn↗

arXiv2011

Percolation Thresholds of the Fortuin-Kasteleyn Cluster for a Potts Gauge Glass Model on Complex Networks: Analytical Results on the Nishimori Line

It was pointed out by de Arcangelis et al. [Europhys. Lett. 14 (1991), 515] that the correct understanding of the percolation phenomenon of the Fortuin-Kasteleyn cluster in the Edwards-Anderson model is important since a dynamical transition, which is characterized by a parameter called the Hamming distance or damage, and the percolation transition are related to a transition for a signal propagating between spins. We show analytically the percolation thresholds of the Fortuin-Kasteleyn cluster for a Potts gauge glass model, which is an extended model of the Edwards-Anderson model, on random graphs with arbitary degree distributions. The results are shown on the Nishimori line. We also show the results for the infinite-range model.

cond-mat.dis-nn↗

arXiv2010

Percolation Thresholds of the Fortuin-Kasteleyn Cluster for the Edwards-Anderson Ising Model on Complex Networks

We analytically show the percolation thresholds of the Fortuin-Kasteleyn cluster for the Edwards-Anderson Ising model on random graphs with arbitrary degree distributions. The results on the Nishimori line are shown. We obtain the results for the +-J model, the diluted +-J model, and the Gaussian model, by applying an extension of a criterion for the random graphs with arbitrary degree distributions. The results for the infinite-range $\pm J$ model and the Sherrington-Kirkpatrick model are also shown.

cond-mat.dis-nn↗

arXiv2003

Transition matrix Monte Carlo method for quantum systems

We propose an efficient method for Monte Carlo simulation of quantum lattice models. Unlike most other quantum Monte Carlo methods, a single run of the proposed method yields the free energy and the entropy with high precision for the whole range of temperature. The method is based on several recent findings in Monte Carlo techniques, such as the loop algorithm and the transition matrix Monte Carlo method. In particular, we derive an exact relation between the DOS and the expectation value of the transition probability for quantum systems, which turns out to be useful in reducing the statistical errors in various estimates.

cond-mat.stat-mech↗

arXiv2002

Novel Monte Carlo algorithms and their applications

We describe a generalized scheme for the probability-changing cluster (PCC) algorithm, based on the study of the finite-size scaling property of the correlation ratio, the ratio of the correlation functions with different distances. We apply this generalized PCC algorithm to the two-dimensional 6-state clock model. We also discuss the combination of the cluster algorithm and the extended ensemble method. We derive a rigorous broad histogram relation for the bond number. A Monte Carlo dynamics based on the number of potential moves for the bond number is proposed, and applied to the three-dimensional Ising and 3-state Potts models.

cond-mat.stat-mech↗

arXiv2002

Broad histogram relation for the bond number and its applications

We discuss Monte Carlo methods based on the cluster (graph) representation for spin models. We derive a rigorous broad histogram relation (BHR) for the bond number; a counterpart for the energy was derived by Oliveira previously. A Monte Carlo dynamics based on the number of potential moves for the bond number is proposed. We show the efficiency of the BHR for the bond number in calculating the density of states and other physical quantities.

cond-mat.stat-mech↗

arXiv2002

Combination of improved multibondic method and the Wang-Landau method

We propose a method for Monte Carlo simulation of statistical physical models with discretized energy. The method is based on several ideas including the cluster algorithm, the multicanonical Monte Carlo method and its acceleration proposed recently by Wang and Landau. As in the multibondic ensemble method proposed by Janke and Kappler, the present algorithm performs a random walk in the space of the bond population to yield the state density as a function of the bond number. A test on the Ising model shows that the number of Monte Carlo sweeps required of the present method for obtaining the density of state with a given accuracy is proportional to the system size, whereas it is proportional to the system size squared for other conventional methods. In addition, the new method shows a better performance than the original Wang-Landau method in measurement of physical quantities.

cond-mat.stat-mech↗

arXiv2001

Three-dimensional antiferromagnetic q-state Potts models: application of the Wang-Landau algorithm

We apply a newly proposed Monte Carlo method, the Wang-Landau algorithm, to the study of the three-dimensional antiferromagnetic q-state Potts models on a simple cubic lattice. We systematically study the phase transition of the models with q=3, 4, 5 and 6. We obtain the finite-temperature phase transition for q= 3 and 4, whereas the transition temperature is down to zero for q=5. For q=6 there exists no order for all the temperatures. We also study the ground-state properties. The size-dependence of the ground-state entropy is investigated. We find that the ground-state entropy is larger than the contribution from the typical configurations of the broken-sublattice-symmetry state for q=3. The same situations are found for q = 4, 5 and 6.

cond-mat.stat-mech↗