Inequalities for the Local Energy of Random Ising Models(Condensed matter: electronic structure and electrical, magnetic, and optical properties)

スポンサーリンク

概要

• 論文の詳細を見る

• We derive a rigorous lower bound on the average local energy for the Ising model with quenched randomness. The result is that the lower bound is given by the average local energy calculated for the isolated case, i.e. in the absence of all other interactions. The only condition for this statement to hold is that the distribution function of the random interaction corresponding to the average local energy under consideration is an even function of randomness (symmetric). All other interactions can be arbitrarily distributed including non-random cases. A non-trivial fact is that any introduction of other interactions to the isolated case always leads to an increase of the average local energy, which is opposite to ferromagnetic systems where the Griffiths inequality holds. Another inequality is proved for asymmetrically distributed interactions: When we consider the value of the thermal average of local energy in the configurational space of randomness, the probability for this value to be lower than that for the isolated case takes a maximum value on the Nishimori line as a function of the temperature. In this sense the system is most stable on the Nishimori line.

• 社団法人日本物理学会の論文
• 2007-07-15

著者

• Aoki Akira

  Department Of Electrical Engineering Nagaoka University Of Technology

• Kitatani Hidetsugu

  Department Of Electrical Engineering Nagaoka University Of Technology

• Nishimori Hidetoshi

  Department Of Physics Tokyo Institute Of Technology

• Nishimori Hidetoshi

  Department Of Physics Facuilty Of Science Tokyo Institute Of Technology

• AOKI Akira

  Department of Biotechnology, Tokyo University of Agriculture and Technology

関連論文

• Ground State of Three-Dimensional Quantum RKKY Spin Glass
• Reweighting Method for Quantum Monte Carlo Simulations with the Negative-Sign Problem
• A Numerical Study of Spin-1/2 Alternating Antiferromagnetic Heisenberg Linear Chains
• High Resolution Solid State ^C NMR Spectroscopy of Polypropylene with Very High Syndiospecificity
• Nonlinear Master Equation Approach to Asymmertrica Neural Networks of the Hopfield-Hemmen Type
• Ferromagnetic Transition of ±J Ising Spin Glass Model on Square Lattice
• Competition between the Neel and the Effective Singlet States in Spin-1/2 Alternating : Heisenberg-Ising Antiferromagnet in One Dimension
• Perturbational Method for the Numerical Evaluation of the Ground-State Energy of the Heisenberg Model
• Germline Mutations of the MEN1 Gene in Japanese Kindred with Multiple Endocrine Neoplasia Type 1
• Nontrivial Phase Behaviour in the Infinite-Range Quantum Mattis Model : General Physics
• Monte Carlo Simulation and Static and Dynamic Critical Behavior of the Plane Rotator Model
• Error Counting in a Quantum Error-correcting Code and the Ground-State Energy of a Spin Glass(General)
• CALCIUM AND POTASSIUM UPTAKE FROM CLAY BY FRUIT TREE ROOTS
• B-84. Surgical Treatment of Arteriovenous Malformation of the Brain
• The Nature of the Specific Heat of Ising Spin Glass
• STUDIES ON CATION EXCHANGE CAPACITY AND CATION ADSORPTION OF FRUIT TREE ROOT
• MEDICO-PEDOLOGICAL STUDIES ON ENDEMICS : CHEMICAL COMPOSITION OF SOILS IN RELATION TO AMYOTROPHIC LATERAL SCLEROSIS IN KII PENINSULA, JAPAN
• A New Type of Argument for the Existence of an Exact Dimer Ground State in S=1/2 Quantum Heisenberg Spin Systems
• Ferromagnetic-Nonferromagnetic Phase Boundary on the Two-Dimensional ±J Ising Model
• Ground State Entanglement in Spin Systems
• Ground State of Quantum Spin Glass with Infinite Range Interactions
• Ground State of Antiferromagnetic Quantum Spin Systems on the Triangular Lattice
• The Spin Wave Theory in Antiferromagnetic Heisenberg Model on Face Centered Cubic Lattice
• Phase Diagram of the p-Spin-Interacting Spin Glass with Ferromagnetic Bias and a Transverse Field in the Infinite-p Limit(General)
• Duality and Multicritical Point of Two-Dimensional Spin Glasses
• CAM Analysis of Dimensionality Crossover
• CAM Analysis of Dimensionality Crossover
• Ground-State Energy of the Heisenberg Model with XY-Like Anisotropy : Condensed Matter and Statistical Physics
• More about the Ground State of Quantum Spin Systems on the Triangular Lattice
• Ground State of Quantum Spin Systems on the Triangular Lattice
• Duality of the Random Model and the Quantum Toric Code
• Reentrant Phenomena in Some Ising Spin Systems-Rigorous Results and Effects of an External Field-
• Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics(General)
• The Shift Exponent of the Layered Square-Lattice Ising Models
• Modified Spin Wave Theory of the Two-Dimensional Frustrated Heisenberg Model
• Statistical-Mechanical Approaches to the Problem of Phase Retrieval by the Q-Ising Model
• Phase Structure of the Random Z_q Models in 2D
• Erbium: YAG Laser, Promising Procedure for Caries Treatment
• Numerical Analysis of Spin-1/2 Alternating Heisenberg-XY Antiferromagnet in One Dimension
• Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices (General)
• Internal Energy of the Potts Model on the Triangular Lattice with Two- and Three-Body Interactions(General)
• Absence of Spin Glass Ordering in Some Random Spin Systems
• Exact Ground-State Energy of the Ising Spin Glass on Strips
• Griffiths Inequalities in the Nishimori Line
• Inequalities for the Local Energy of Random Ising Models(Condensed matter: electronic structure and electrical, magnetic, and optical properties)
• Concentration of the Multicritical Points in the ±J Ising Models
• Determination of the Critical Points of Antiferromagnetic Ising Model with Next Nearest Neighbour Interactions on the Triangular Lattice
• Griffiths Inequalities for Ising Spin Glasses on the Nishimori Line
• The Verticality of the Ferromagnetic-Spin Glass Phase Boundary of the ^+_-J Ising Model in the p-T Plane
• Non-Universal Critical Behavior in the Ferromagnetic Transition of the ±J Ising Model
• Coherent-Anomaly Method Applied to the Quantum Heisenberg Model
• Coherent-Anomaly Method Applied to the Lattice Obtained by the Dual Transformation in the Ising Model
• Theory of the Resonating Valence Bond in Quantum Spin System
• Antiferromagnetic Triangular Ising Model with Ferromagnetic Next Nearest Neighbor Interactions : Transfer Matrix Method
• Some Properties of Eigenvalues and Eigenfunctions for Finite Systems on the Antiferromagnetic Heisenberg Model
• The Cluster Decomposition Approach to Finite Quantum Spin Systems
• Spin Wave Theory for a Frustrated Antiferromagnetic Heisenberg Model on a Square Lattice
• The Critical Exponent v along the Ferromagnetic-Nonferromagnetic Phase Boundary in the Two-Dimensional ±-J Ising Model
• Dimer State in Quantum Spin Systems
• The Critical Exponent η of the Three-Dimensional ±Jlsing Model by the Transfer Matrix Method
• Note on Twisted Order in the Frustrated Quantum Heisenberg Model
• Long-Range Order in the Frustrated XXZ Model
• Statistical Mechanics of Image Restoration by the Plane Rotator Model
• Numerical Diagonalization of Quantum Spin Hamiltonians
• Distribution of Yang-Lee Zeros of the ±J Ising Model
• Ground-State Long-Range Order in the Two-Dimensional XXZ Model
• Long-Range Order in Antiferromagnetic Quantum Spin Systems
• Phase Diagram of the ±J Ising Model in Two Dimensions
• Phase Diagram and Critical Exponents of the ±J Ising Model in Finite Dimensions by Monte Carlo Renormalization Group
• High-Temperature Dynamics of Spin Glasses
• Microcanonical Analysis of Spin Glasses Using Gauge Symmetry
• Exact Results on the Ising Spin Glass in Finite Dimensions
• One-Dimensional Critical Exponent η as a Function of the Spin Quantum Number and Anisotropy : Progress Letters
• Geometry-Induced Phase Transtiton in the ±J Ising Model
• Quantum Effects in Neural Networks
• Magnetization Process of the Spin-1/2 Antiferromagnetic Ising-Like Heisenberg Model on the Triangular Lattice
• Internal Energy, Specific Heat and Correlation Function of the Bond-Random Ising Model
• Gauge Glass Ordering in Two Dimensions
• Exact Ground-State Energies of the Random-Field Ising Chain and Ladder(General)
• Nonequilibrium Work on Spin Glasses in Longitudinal and Transverse Fields
• CHEMICAL AND MINERALOGICAL STUDIES ON THE CITRUS SOILS IN WAKAYAMA PREFECTURE, JAPAN
• Ensemble Inequivalence in the Spherical Spin Glass Model with Nonlinear Interactions
• Optimum Decoding Temperature for Error-Correcting Codes
• Boundary between the Ferromagnetic and Spin Glass Phases
• Nonequilibrium Relations for Spin Glasses with Gauge Symmetry
• Phase Structure of the Random Z_q Models in 2D
• Ground State Entanglement in Spin Systems
• Duality of the Random Model and the Quantum Toric Code
• Exact Ground-State Energies of the Random-Field Ising Chain and Ladder
• The Nature of the Specific Heat of Ising Spin Glass
• Griffiths Inequalities in the Nishimori Line
• Griffiths Inequalities for Ising Spin Glasses on the Nishimori Line
• Addendum to Phase Diagram and Critical Exponents of the $\pm J$ Ising Model in Finite Dimensions by Monte Calro Renormalization Group [56 (1987) 1568]
• Energy Gap at First-Order Quantum Phase Transitions: An Anomalous Case
• Gauge Theory for Quantum Spin Glasses(General)

もっと見る 閉じる

スポンサーリンク