Kernel method for corrections to scaling

Abstract

Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are corrections to scaling in many cases, and then the inference problem becomes ill-posed by an uncontrollable irrelevant scaling variable. We propose a new kernel method based on Gaussian process regression to fix this problem generally. We test the performance of the new kernel method for some example cases. In all cases, when the precision of the example data increases, inference results of the new kernel method correctly converge. Because there is no limitation in the new kernel method for the scaling function even with corrections to scaling, unlike in the conventional method, the new kernel method can be widely applied to real data in critical phenomena.

8 pages, 5 figures, the reference code of this new method is prepared at http://kenjiharada.github.io/BSA/

References in corpus (20)

• MCMC using Hamiltonian dynamics
• "Deconfined" quantum critical points
• The ALPS project release 2.0: Open source software for strongly correlated systems
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• Corrections to scaling at the Anderson transition
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• A lattice model for the SU(N) Neel-VBS quantum phase transition at large N
• Fate of CP(N-1) fixed points with q-monopoles
• Deconfined criticality flow in the Heisenberg model with ring-exchange interactions
• Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N
• Néel to valence-bond solid transition on the honeycomb lattice: Evidence for deconfined criticality
• Bayesian Inference in the Scaling Analysis of Critical Phenomena
• A Scaling Relation for Dangerously Irrelevant Symmetry-Breaking Fields
• Path-integral Monte Carlo method for the local Z_2 Berry phase
• Minimum vertex cover problems on random hypergraphs: replica symmetric solution and a leaf removal algorithm
• Thermal Phase Transition of Generalized Heisenberg Models for SU(N) Spins on Square and Honeycomb Lattices
• Monte Carlo simulations of the three-dimensional XY spin glass focusing on the chiral and the spin order
• Evidence of one-step replica symmetry breaking in a three-dimensional Potts glass model
• Window measurements of simulations in random systems

Cited by in corpus (27)

• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Detecting signals of weakly first-order phase transitions in two-dimensional Potts models
• Competition between spin liquids and valence-bond order in the frustrated spin-$1/2$ Heisenberg model on the honeycomb lattice
• Phase transitions and ordering structures of a model of chiral helimagnet in three dimensions
• New easy-plane ${\mathbb{CP}}^{N-1}$ fixed points
• Diagnosing weakly first-order phase transitions by coupling to order parameters
• Magnetic three states of matter: A quantum Monte Carlo study of spin liquids
• Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes
• Disorder-induced Revival of the Bose-Einstein Condensation in Ni(Cl${}_{1-x}$Br${}_x$)${}_2$-4SC(NH${}_2$)${}_2$ at High Magnetic Fields
• Competing Bose-Glass physics with disorder-induced Bose-Einstein condensation in the doped $S=1$ antiferromagnet Ni(Cl${}_{1-x}$Br${}_x$)${}_2$-4SC(NH${}_2$)${}_2$ at high magnetic fields
• Quantum Monte Carlo study of superfluid density in quasi-one-dimensional hard-core bosons: Effect of suppression of phase slippage
• Non-monotonic behavior of the Binder Parameter in the discrete spin systems
• Corner transfer matrix renormalization group analysis of the two-dimensional dodecahedron model
• Critical exponents in coupled phase-oscillator models on small-world networks
• Neural Network Approach to Scaling Analysis of Critical Phenomena
• Correlation Effects in a Simplified Bilayer Two-Orbital Hubbard Model at Half Filling
• Effect of Constraint Relaxation on the Minimum Vertex Cover Problem in Random Graphs
• Validity of Harris criterion for two-dimensional quantum spin systems with quenched disorder
• MateriApps LIVE! and MateriApps Installer: Environment for starting and scaling up materials science simulations
• Ground-state phase diagram of S = 1/2 Heisenberg model on 2D square-hexagon-octagon lattice
• Phase transitions and remnants of fractionalization at finite temperature in the triangular lattice quantum loop model
• Bubble formation in active binary mixture model
• An Efficient Monte-Carlo Method to Make a Geometric Graph with a Fixed Connectivity
• Improvement of analysis for relaxation of fluctuations by the use of Gaussian process regression and extrapolation method
• Dimensional Reduction of Dynamical Systems by Machine Learning: Automatic Generation of the Optimum Extensive Variables and Their Time-Evolution Map
• Off-Diagonal dipolar interactions in the mixed Ising--XY magnet $LiH{o}_{x}E{r}_{1-x}{F}_4$
• Faithfulness of Real-Space Renormalization Group Maps