Window measurements of simulations in random systems

Abstract

Numerical studies in random systems are plagued with strong finite-size effects and boundary effects. We introduce a window-measurement method as a practical solution to these difficulties. We observe physical quantities only within a subsystem located in the midst of a whole system and scale them with the correlation length estimated in the subsystem. Both equilibrium data and nonequilibrium data with different system sizes and different window sizes fall onto a single scaling function. It suggests that the correction-to-scaling terms become very small. We confirm the validity in the $\pm J$ Heisenberg spin glass model in three dimensions. The spin-glass and chiral-glass transition temperatures are estimated to be very close to each other.

arXiv comment5 pages, 4 figures

References in corpus (25)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet
• Single spin- and chiral-glass transition in vector spin glasses in three-dimensions
• Bayesian Inference in the Scaling Analysis of Critical Phenomena
• Chiral-glass transition and replica symmetry breaking of a three-dimensional Heisenberg spin glass
• Simplicity of State and Overlap Structure in Finite-Volume Realistic Spin Glasses
• Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis
• Large-scale Monte Carlo simulation of two-dimensional classical XY model using multiple GPUs
• 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
• An Extended Scaling Scheme for Critically Divergent Quantities in Ferromagnets and Spin Glasses
• 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
• Stiffness of the Heisenberg Spin-Glass Model at Zero- and Finite-Temperatures in Three Dimensions
• Small Window Overlaps Are Effective Probes of Replica Symmetry Breaking in 3D Spin Glasses
• Weak universality of spin-glass transitions in three-dimensional $\pm J$ models
• Dynamical AC study of the critical behavior in Heisenberg spin glasses
• Dynamical Critical Phenomena in three-dimensional Heisenberg Spin Glasses
• Uniform Magnetic Order in a Ferromagnetic-Antiferromagnetic Random Alternating Quantum Spin Chain
• Finite spin-glass transition of the $\pm J$ XY model in three dimensions
• The antiferromagnetic order in an F-AF random alternating quantum spin chain : (CH_3)_2 CHNH_3 Cu(Cl_x Br_{1-x})_3
• Nonequilibrium dynamic-correlation-length scaling method

Cited by in corpus (4)

• Kernel method for corrections to scaling
• From measurements to inferences of physical quantities in numerical simulations
• A strategy for solving difficulties in spin-glass simulations
• Entanglement Entropy of the Two-Dimensional +-J Ising Model on the Nishimori Line