arXiv subjects

Hidetoshi Nishimori

Publications and source records attributed to Hidetoshi Nishimori.

At least 73 records · Page 4Linked to original sources

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

Nonequilibrium work on spin glasses in longitudinal and transverse fields

We derive a number of exact relations between equilibrium and nonequilibrium quantities for spin glasses in external fields using the Jarzynski equality and gauge symmetry. For randomly-distributed longitudinal fields, a lower bound is established for the work done on the system in nonequilibrium processes, and identities are proven to relate equilibrium and nonequilibrium quantities. In the case of uniform transverse fields, identities are proven between physical quantities and exponentiated work done to the system at different parts of the phase diagram with the context of quantum annealing in mind. Additional relations are given, which relate the exponentiated work in quantum and simulated (classical) annealing. It is also suggested that the Jarzynski equality may serve as a guide to develop a method to perform quantum annealing under non-adiabatic conditions.

cond-mat.dis-nn↗

arXiv2011

Real-space renormalization group for the transverse-field Ising model in two and three dimensions

The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization group method. The basic strategy is a generalization of a method developed for the one-dimensional case, which exploits the exact invariance of the model under renormalization and is known to give the exact values of the critical point and critical exponent $ν$. The resulting values of the critical exponent $ν$ in two and three dimensions are in good agreement with those for the classical Ising model in three and four dimensions. This is the first example in which a real-space renormalization group on (2+1)- and (3+1)-dimensional Bravais lattices yields accurate estimates of the critical exponents.

cond-mat.stat-mech↗

arXiv2011

Random-field p-spin glass model on regular random graphs

We investigate in detail the phase diagrams of the p-body +/-J Ising model with and without random fields on random graphs with fixed connectivity. One of our most interesting findings is that a thermodynamic spin glass phase is present in the three-body purely ferromagnetic model in random fields, unlike for the canonical two-body interaction random-field Ising model. We also discuss the location of the phase boundary between the paramagnetic and spin glass phases that does not depend on the change of the ferromagnetic bias. This behavior is explained by a gauge transformation, which shows that gauge-invariant properties generically do not depend on the strength of the ferromagnetic bias for the +/-J Ising model on regular random graphs.

cond-mat.dis-nn↗

arXiv2011

Ensemble Inequivalence in the Ferromagnetic p-spin Model in Random Fields

We study the effect that randomness has on long-range interacting systems by using the ferromagnetic Ising model with $p$-body interactions in random fields. The case with p=2 yields a phase diagram similar to that of previously studied models and shows known features that inequivalence of the canonical and microcanonical ensembles brings with it, for example negative specific heat in a narrow region of the phase diagram. When p>2, however, the canonical phase diagram is completely different from the microcanonical one. The temperature does not necessarily determine the microcanonical phases uniquely, and thus the ferromagnetic and paramagnetic phases are not separated in such a region of a conventional phase diagram drawn with the temperature and field strength as the axes. Below a certain value of the external field strength, part of the ferromagnetic phase has negative specific heat. For large values of the external field strength the ergodicity is broken before the phase transition occurs for p>2. Moreover, for p>2, the Maxwell construction cannot be derived in a consistent manner and therefore, in contrast to previous cases with negative specific heat, the Maxwell construction does not bridge the gap between the ensembles.

cond-mat.dis-nn↗

arXiv2011

Microcanonical Analysis of Spin Glasses Using Gauge Symmetry

We apply the method of gauge transformation to spin glasses under the microcanonical ensemble to study the possibility of ensemble inequivalence in systems with long-range interactions and quenched disorder. It is proved that all the results derived under the canonical ensemble on the Nishimori line (NL) can be reproduced by the microcanonical ensemble irrespective of the range of interactions. This establishes that ensemble inequivalence should take place away from the NL if it happens in spin glasses. It is also proved on the NL that the microcanonical configurational average of the energy as a function of temperature is exactly equal to the average energy in the canonical ensemble for any finite-size systems with Gaussian disorder. In this sense, ensembles are equivalent even for finite systems.

cond-mat.dis-nn↗

arXiv2010

Accelerated Stochastic Sampling of Discrete Statistical Systems

We propose a method to reduce the relaxation time towards equilibrium in stochastic sampling of complex energy landscapes in statistical systems with discrete degrees of freedom by generalizing the platform previously developed for continuous systems. The method starts from a master equation, in contrast to the Fokker-Planck equation for the continuous case. The master equation is transformed into an imaginary-time Schrödinger equation. The Hamiltonian of the Schrödinger equation is modified by adding a projector to its known ground state. We show how this transformation decreases the relaxation time and propose a way to use it to accelerate simulated annealing for optimization problems. We implement our method in a simplified kinetic Monte Carlo scheme and show an acceleration by an order of magnitude in simulated annealing of the symmetric traveling salesman problem. Comparisons of simulated annealing are made with the exchange Monte Carlo algorithm for the three-dimensional Ising spin glass. Our implementation can be seen as a step toward accelerating the stochastic sampling of generic systems with complex landscapes and long equilibration times.

cond-mat.stat-mech↗

arXiv2010

Quantum Annealing with Jarzynski Equality (CCP2009)

We show a practical application of an well-known nonequilibrium relation, the Jarzynski equality, in quantum computation. Its implementation may open a way to solve combinatorial optimization problems, minimization of a real single-valued function, cost function, with many arguments. It has been disclosed that the ordinary quantum computational algorithm to solve a kind of hard optimization problems, has a bottleneck that its computational time is restricted to be extremely slow without relevant errors. However, by our novel strategy shown in the present study, we might overcome such a difficulty.

quant-ph↗

arXiv2010

Distribution of partition function zeros of the $\pm J$ model on the Bethe lattice

The distribution of partition function zeros is studied for the $\pm J$ model of spin glasses on the Bethe lattice. We find a relation between the distribution of complex cavity fields and the density of zeros, which enables us to obtain the density of zeros for the infinite system size by using the cavity method. The phase boundaries thus derived from the location of the zeros are consistent with the results of direct analytical calculations. This is the first example in which the spin glass transition is related to the distribution of zeros directly in the thermodynamical limit. We clarify how the spin glass transition is characterized by the zeros of the partition function. It is also shown that in the spin glass phase a continuous distribution of singularities touches the axes of real field and temperature.

cond-mat.dis-nn↗

arXiv2010

Quantum annealing: An introduction and new developments

Quantum annealing is a generic algorithm using quantum-mechanical fluctuations to search for the solution of an optimization problem. The present paper first reviews the fundamentals of quantum annealing and then reports on preliminary results for an alternative method. The review part includes the relationship of quantum annealing with classical simulated annealing. We next propose a novel quantum algorithm which might be available for hard optimization problems by using a classical-quantum mapping as well as the Jarzynski equality introduced in nonequilibrium statistical physics.

cond-mat.dis-nn↗

arXiv2010

Nonequilibrium relations in spin glasses

The applications of nonequilbrium relations such as the Jarzynski equality and the fluctuation theorem to spin glasses are considered. The spin glass is a basic platform where we consider an application of an approximate solver of combinatorial optimization problems, simulated annealing. We find a novel relationship between an average through a nonequilibrium process where the temperature changes as in simulated annealing and a thermal average in equilibrium with different amounts of quenched randomness. The results shown in the present study may serve as an alternative way to overcome critical slowing down in spin glasses. It means that this way may mitigate difficulties in several hard optimization problems.

cond-mat.dis-nn↗

arXiv2010

Zero-Temperature Complex Replica Zeros of the $\pm J$ Ising Spin Glass on Mean-Field Systems and Beyond

Zeros of the moment of the partition function $[Z^n]_{\bm{J}}$ with respect to complex $n$ are investigated in the zero temperature limit $β\to \infty$, $n\to 0$ keeping $y=βn \approx O(1)$. We numerically investigate the zeros of the $\pm J$ Ising spin glass models on several Cayley trees and hierarchical lattices and compare those results. In both lattices, the calculations are carried out with feasible computational costs by using recursion relations originated from the structures of those lattices. The results for Cayley trees show that a sequence of the zeros approaches the real axis of $y$ implying that a certain type of analyticity breaking actually occurs, although it is irrelevant for any known replica symmetry breaking. The result of hierarchical lattices also shows the presence of analyticity breaking, even in the two dimensional case in which there is no finite-temperature spin-glass transition, which implies the existence of the zero-temperature phase transition in the system. A notable tendency of hierarchical lattices is that the zeros spread in a wide region of the complex $y$ plane in comparison with the case of Cayley trees, which may reflect the difference between the mean-field and finite-dimensional systems.

cond-mat.dis-nn↗

arXiv2010

Non-equilibrium Relations for Spin Glasses with Gauge Symmetry

We study the applications of non-equilibrium relations such as the Jarzynski equality and fluctuation theorem to spin glasses with gauge symmetry. It is shown that the exponentiated free-energy difference appearing in the Jarzynski equality reduces to a simple analytic function written explicitly in terms of the initial and final temperatures if the temperature satisfies a certain condition related to gauge symmetry. This result is used to derive a lower bound on the work done during the non-equilibrium process of temperature change. We also prove identities relating equilibrium and non-equilibrium quantities. These identities suggest a method to evaluate equilibrium quantities from non-equilibrium computations, which may be useful to avoid the problem of slow relaxation in spin glasses.

cond-mat.dis-nn↗

arXiv2009

Multicritical point of spin glasses

We present a theoretical framework to accurately calculate the location of the multicritical point in the phase diagram of spin glasses. The result shows excellent agreement with numerical estimates. The basic idea is a combination of the duality relation, the replica method, and the gauge symmetry. An additional element of the renormalization group, in particular in the context of hierarchical lattices, leads to impressive improvements of the predictions.

cond-mat.dis-nn↗

arXiv2009

Ground-state statistics from annealing algorithms: Quantum vs classical approaches

We study the performance of quantum annealing for systems with ground-state degeneracy by directly solving the Schrödinger equation for small systems and quantum Monte Carlo simulations for larger systems. The results indicate that naive quantum annealing using a transverse field may not be well suited to identify all degenerate ground-state configurations, although the value of the ground-state energy is often efficiently estimated. An introduction of quantum transitions to all states with equal weights is shown to greatly improve the situation but with a sacrifice in the annealing time. We also clarify the relation between the spin configurations in the degenerate ground states and the probabilities that those states are obtained by quantum annealing. The strengths and weaknesses of quantum annealing for problems with degenerate ground states are discussed in comparison with classical simulated annealing.

quant-ph↗

arXiv2009

Analytical evidence for the absence of spin glass transition on self-dual lattices

We show strong evidence for the absence of a finite-temperature spin glass transition for the random-bond Ising model on self-dual lattices. The analysis is performed by an application of duality relations, which enables us to derive a precise but approximate location of the multicritical point on the Nishimori line. This method can be systematically improved to presumably give the exact result asymptotically. The duality analysis, in conjunction with the relationship between the multicritical point and the spin glass transition point for the symmetric distribution function of randomness, leads to the conclusion of the absence of a finite-temperature spin glass transition for the case of symmetric distribution. The result is applicable to the random bond Ising model with $\pm J$ or Gaussian distribution and the Potts gauge glass on the square, triangular and hexagonal lattices as well as the random three-body Ising model on the triangular and the Union-Jack lattices and the four dimensional random plaquette gauge model. This conclusion is exact provided that the replica method is valid and the asymptotic limit of the duality analysis yields the exact location of the multicritical point

cond-mat.dis-nn↗

arXiv2009

Multicritical points for the spin glass models on hierarchical lattices

The locations of multicritical points on many hierarchical lattices are numerically investigated by the renormalization group analysis. The results are compared with an analytical conjecture derived by using the duality, the gauge symmetry and the replica method. We find that the conjecture does not give the exact answer but leads to locations slightly away from the numerically reliable data. We propose an improved conjecture to give more precise predictions of the multicritical points than the conventional one. This improvement is inspired by a new point of view coming from renormalization group and succeeds in deriving very consistent answers with many numerical data.

cond-mat.dis-nn↗

arXiv2009

Reentrant and Forward Phase Diagrams of the Anisotropic Three-Dimensional Ising Spin Glass

The spatially uniaxially anisotropic d=3 Ising spin glass is solved exactly on a hierarchical lattice. Five different ordered phases, namely ferromagnetic, columnar, layered, antiferromagnetic, and spin-glass phases, are found in the global phase diagram. The spin-glass phase is more extensive when randomness is introduced within the planes than when it is introduced in lines along one direction. Phase diagram cross-sections, with no Nishimori symmetry, with Nishimori symmetry lines, or entirely imbedded into Nishimori symmetry, are studied. The boundary between the ferromagnetic and spin-glass phases can be either reentrant or forward, that is either receding from or penetrating into the spin-glass phase, as temperature is lowered. However, this boundary is always reentrant when the multicritical point terminating it is on the Nishimori symmetry line.

cond-mat.dis-nn↗