A New Method to Calculate the Spin-Glass Order Parameter of the Two-Dimensional +/-J Ising Model

A new method to numerically calculate the $n$th moment of the spin overlap of the two-dimensional $\pm J$ Ising model is developed using the identity derived by one of the authors (HK) several years ago. By using the method, the $n$th moment of the spin overlap can be calculated as a simple average of the $n$th moment of the total spins with a modified bond probability distribution. The values of the Binder parameter etc have been extensively calculated with the linear size, $L$, up to L=23. The accuracy of the calculations in the present method is similar to that in the conventional transfer matrix method with about $10^{5}$ bond samples. The simple scaling plots of the Binder parameter and the spin-glass susceptibility indicate the existence of a finite-temperature spin-glass phase transition. We find, however, that the estimation of $T_{\rm c}$ is strongly affected by the corrections to scaling within the present data ($L\leq 23$). Thus, there still remains the possibility that $T_{\rm c}=0$, contrary to the recent results which suggest the existence of a finite-temperature spin-glass phase transition.Comment: 10 pages,8 figures: final version to appear in J. Phys.

Griffiths Inequalities for Ising Spin Glasses on the Nishimori Line

The Griffiths inequalities for Ising spin glasses are proved on the Nishimori line with various bond randomness which includes Gaussian and $\pm J$ bond randomness. The proof for Ising systems with Gaussian bond randomness has already been carried out by Morita et al, which uses not only the gauge theory but also the properties of the Gaussian distribution, so that it cannot be directly applied to the systems with other bond randomness. The present proof essentially uses only the gauge theory, so that it does not depend on the detail properties of the probability distribution of random interactions. Thus, the results obtained from the inequalities for Ising systems with Gaussian bond randomness do also hold for those with various bond randomness, especially with $\pm J$ bond randomness.Comment: 13pages. Submitted to J. Phys. Soc. Jp

Application of LaBr3 detector for neutron resonance densitometry

A method to determine the amount of nuclear materials in melted fuel resulting from a nuclear accident such as the one occurred at the Fukushima Daiichi nuclear power plants has not yet been established. The problem is complex due to the expected presence of 10B and other strong neutron absorbing impurities. For this reason, neutron resonance densitometry, combining neutron resonance transmission analysis and neutron capture analysis, is proposed and a feasibility study has been defined. In this contribution a method to account for the presence of 10B is presented and investigated. The study includes GEANT4 simulations to study the performance of a new well type gamma-ray detector based on LaBr3 scintillators. In the design of the detector the main emphasis was on the capability to separate the full energy peak corresponding to the 478-keV gamma ray resulting from the 10B(n,αγ) reaction from the contribution of the 662-keV gamma ray due to the decay of 137Cs. In addition, experiments have been carried out at the time-of-flight facility GELINA of the EC-JRC-IRMM to test the capabilities of a LaBr3 detector for NRCA applications, in particular to determine impurities present in the melted fuel. A neutron resonance capture gamma-ray experiment with a natSe sample was performed using a LaBr3 scintillator in parallel with a Ge-detector. The results of these measurements demonstrate that a LaBr3 detector is suitable for NRCA as a part of neutron resonance densitometry.JRC.D.4-Standards for Nuclear Safety, Security and Safeguard

Topological quantum memory

We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of these protocols. An order-disorder phase transition occurs in this system at a nonzero critical value of the error rate; if the error rate is below the critical value (the accuracy threshold), encoded information can be protected arbitrarily well in the limit of a large code block. This phase transition can be accurately modeled by a three-dimensional Z_2 lattice gauge theory with quenched disorder. We estimate the accuracy threshold, assuming that all quantum gates are local, that qubits can be measured rapidly, and that polynomial-size classical computations can be executed instantaneously. We also devise a robust recovery procedure that does not require measurement or fast classical processing; however for this procedure the quantum gates are local only if the qubits are arranged in four or more spatial dimensions. We discuss procedures for encoding, measurement, and performing fault-tolerant universal quantum computation with surface codes, and argue that these codes provide a promising framework for quantum computing architectures.Comment: 39 pages, 21 figures, REVTe

Proposal of neutron resonance densitometry for particle like debris of melted fuel using NRTA and NRCA

Neutron resonance densitometry (NRD) has been proposed to quantify nuclear materials in particle-like debris of melted fuel formed in a severe accident of nuclear reactors such as the Fukushima Daiichi nuclear power plants. NRD is a method that combines NRTA (neutron resonance transmission analysis) and NRCA (neutron resonance capture analysis) using a pulsed neutron generator and the TOF (time of flight) technique. NRTA is used to quantify the amount of Pu and U isotopes. NRCA is used to identify matrix materials, such as B and Fe, which are present in the melted fuel. A special gamma-ray spectrometer has been designed to apply NRCA in the presence of highly radioactive materials. The applicability of the NRD method has been studied using Monte Carlo simulations and neutron TOF experiments at the GELINA facility of the EC-JRC-IRMM. We conclude that NRD has a potential to determine the quantities of Pu and U isotopes in particle-like debris of melted fuel with counting statistics uncertainties less than 1%, even in the presence of 2.5 w% natB and 9 w% 56Fe.JRC.D.4-Standards for Nuclear Safety, Security and Safeguard

Aging Relation for Ising Spin Glasses

We derive a rigorous dynamical relation on aging phenomena -- the aging relation -- for Ising spin glasses using the method of gauge transformation. The waiting-time dependence of the auto-correlation function in the zero-field-cooling process is equivalent with that in the field-quenching process. There is no aging on the Nishimori line; this reveals arguments for dynamical properties of the Griffiths phase and the mixed phase. The present method can be applied to other gauge-symmetric models such as the XY gauge glass.Comment: 9 pages, RevTeX, 2 postscript figure

Characterization of nuclear material by Neutron Resonance Transmission Analysis

The use of Neutron Resonance Transmission Analysis for the characterization of nuclear materials is discussed. The method, which relies on resonance structures in neutron-induced reaction cross sections, can be applied as a non-destructive method to characterise complex nuclear materials such as melted fuel resulting from a severe nuclear accident. Results of a demonstration experiment at the GELINA facility reveal that accurate data can be obtained at a compact facility even in the case of strong overlapping resonances

The two-dimensional random-bond Ising model, free fermions and the network model

We develop a recently-proposed mapping of the two-dimensional Ising model with random exchange (RBIM), via the transfer matrix, to a network model for a disordered system of non-interacting fermions. The RBIM transforms in this way to a localisation problem belonging to one of a set of non-standard symmetry classes, known as class D; the transition between paramagnet and ferromagnet is equivalent to a delocalisation transition between an insulator and a quantum Hall conductor. We establish the mapping as an exact and efficient tool for numerical analysis: using it, the computational effort required to study a system of width $M$ is proportional to $M^{3}$, and not exponential in $M$ as with conventional algorithms. We show how the approach may be used to calculate for the RBIM: the free energy; typical correlation lengths in quasi-one dimension for both the spin and the disorder operators; even powers of spin-spin correlation functions and their disorder-averages. We examine in detail the square-lattice, nearest-neighbour $\pm J$ RBIM, in which bonds are independently antiferromagnetic with probability $p$, and ferromagnetic with probability $1-p$. Studying temperatures $T\geq 0.4J$, we obtain precise coordinates in the $p-T$ plane for points on the phase boundary between ferromagnet and paramagnet, and for the multicritical (Nishimori) point. We demonstrate scaling flow towards the pure Ising fixed point at small $p$, and determine critical exponents at the multicritical point.Comment: 20 pages, 25 figures, figures correcte

NRD Demonstration Experiments at GELINA

Neutron Resonance Densitometry (NRD), a non-destructive analysis method, was presented. The method has been developed to quantify special nuclear material (SNM) in debris of melted fuel that will be produced during the decommissioning of the Fukushima Daiichi nuclear power plants. The method is based on Neutron Resonance Transmission Analysis (NRTA) and Neutron Resonance Capture Analysis combined with Prompt Gamma–ray analysis (NRCA/PGA). The quantification of SNM relies on the NRTA results. The basic principles of NRD, which are based on well-established methodologies for neutron resonance spectroscopy, have been explained. To develop NRD for the characterization of rock- and particle like heterogeneous samples a JAEA/JRC collaboration has been established. As part of this collaboration a NRD demonstration workshop was organized at the time-of-flight facility GELINA of the JRC-IRMM in Geel (B). The potential of NRD was demonstrated by measurements on a complex mixture of different elements. It was demonstrated that the elemental composition of an unknown sample predicted by NRTA deviated on average by less than 2% from the declared value. In addition the potential to identify the presence of light elements by NRCA/PGA was shown.JRC.D.4-Standards for Nuclear Safety, Security and Safeguard

Development of neutron resonance densitometry at the GELINA TOF facility

Neutrons can be used as a tool to study properties of materials and objects. An evolving activity in this field concerns the existence of resonances in neutron induced reaction cross sections. These resonance structures are the basis of two analytical methods which have been developed at the EC-JRC-IRMM: Neutron Resonance Capture Analysis (NRCA) and Neutron Resonance Transmission Analysis (NRTA). They have been applied to determine the elemental composition of archaeological objects and to characterize nuclear reference materials. A combination of NRTA and NRCA together with Prompt Gamma Neutron Analysis, referred to as Neutron Resonance Densitometry (NRD), is being studied as a non-destructive method to characterize particle-like debris of melted fuel that is formed in severe nuclear accidents such as the one which occurred at the Fukushima Daiichi nuclear power plants. This study is part of a collaboration between JAEA and EC-JRC-IRMM. In this contribution the basic principles of NRTA and NRCA are explained based on the experience in the use of these methods at the time-of-flight facility GELINA of the EC-JRC-IRMM. Specific problems related to the analysis of samples resulting from melted fuel are discussed. The programme to study and solve these problems is described and results of a first measurement campaign at GELINA are given.JRC.D.4-Standards for Nuclear Safety, Security and Safeguard