A strategy for solving difficulties in spin-glass simulations

Abstract

A spin-glass transition has been investigated for a long time but we have not yet reached a conclusion due to difficulties in the simulations. They are slow dynamics, strong finite-size effects, and sample-to-sample dependences. We clarified that these difficulties are mainly caused by a competition between the spin-glass order and the boundary conditions. We also found that the spin-glass order grows fast and reaches the lattice boundary within a very short Monte Carlo step. A key to solve the difficulties is to eliminate the boundary effect first. It was made possible by a dynamic scaling analysis on nonequilibrium relaxation functions in a large-size and short-time regime. The observed quantity was also found to be self-averaging in a limit of large replica number. The spin-glass transition and the chiral-glass transition was clarified to occur at the same temperature in the Heisenberg spin-glass model in three dimensions. The estimated critical exponent $\nu$ agrees with the experimental result.

arXiv comment10 pages, 10 figures

References in corpus (37)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Quantum Annealing in the Transverse Ising Model
• Off-Equilibrium Dynamics in Finite-Dimensional Spin Glass Models
• Violation of the Fluctuation Dissipation Theorem in Finite Dimensional Spin Glasses
• Single spin- and chiral-glass transition in vector spin glasses in three-dimensions
• Extraction of the Spin Glass Correlation Length
• Bayesian Inference in the Scaling Analysis of Critical Phenomena
• Nonequilibrium spin glass dynamics from picoseconds to 0.1 seconds
• Chiral-glass transition and replica symmetry breaking of a three-dimensional Heisenberg spin glass
• Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis
• The spin glass transition of the three dimensional Heisenberg spin glass
• Large-scale Monte Carlo simulations of the isotropic three-dimensional Heisenberg spin glass
• Spin-Glass and Chiral-Glass Transitions in a $\pm J$ Heisenberg Spin-Glass Model in Three Dimensions
• Chirality scenario of the spin-glass ordering
• Numerical Study on Aging Dynamics in the 3D Ising Spin-Glass Model. II. Quasi-Equilibrium Regime of Spin Auto-Correlation Function
• Numerical evidence of the spin-chirality decoupling in the three-dimensional Heisenberg spin glass
• Nature of the phase transition of the three-dimensional isotropic Heisenberg spin glass
• Aging Dynamics of the Heisenberg Spin Glass
• Monte Carlo studies of the chiral and spin orderings of the three-dimensional Heisenberg spin glass
• Aging rate of spin glasses from simulations matches experiments
• Stiffness of the Heisenberg Spin-Glass Model at Zero- and Finite-Temperatures in Three Dimensions
• Dynamical scaling in Ising and vector spin glasses
• Testing statics-dynamics equivalence at the spin-glass transition in three dimensions
• Weak universality of spin-glass transitions in three-dimensional $\pm J$ models
• Infinitesimal incommensurate stripe phase in an axial next-nearest-neighbor Ising model in two dimensions
• Dynamical AC study of the critical behavior in Heisenberg spin glasses
• Heisenberg Spin Glass Experiments and the Chiral Ordering Scenario
• Off-equilibrium finite-size method for critical behavior analyses
• Dynamical Critical Phenomena in three-dimensional Heisenberg Spin Glasses
• Uniform Magnetic Order in a Ferromagnetic-Antiferromagnetic Random Alternating Quantum Spin Chain
• The antiferromagnetic order in an F-AF random alternating quantum spin chain : (CH_3)_2 CHNH_3 Cu(Cl_x Br_{1-x})_3
• Finite spin-glass transition of the $\pm J$ XY model in three dimensions
• A Simultaneous Magneto-Dielectric Phase Transition in RbCoBr${}_3$
• The out-equilibrium 2D Ising spin glass: almost, but not quite, a free-field theory
• Nonequilibrium dynamic-correlation-length scaling method
• From measurements to inferences of physical quantities in numerical simulations
• Window measurements of simulations in random systems

Cited by in corpus (4)

• Monte Carlo studies of the spin-chirality decoupling in the three-dimensional Heisenberg spin glass
• Spin-glass dynamics: experiment, theory and simulation
• q-Gaussian Crossover in Overlap Spectra towards 3D Edwards-Anderson Criticality
• Dynamical scaling method improved by a deep learning approach