Extracting critical exponents by finite-size scaling with convolutional neural networks

Finite-size scaling and critical exponents in critical relaxation.

We simulate the critical relaxation process of the two-dimensional Ising model with the initial state both completely disordered or completely ordered. Results of a new method to measure both the dynamic and static critical exponents are reported, based on the finite size scaling for the dynamics at the early time. From the time-dependent Binder cumulant, the dynamical exponent z is extracted i...

Finite Size Scaling in Neural Networks

We demonstrate that the fraction of pattern sets that can be stored in singleand hidden-layer perceptrons exhibits finite size scaling. This feature allows one to estimate the critical storage capacity ac from simulations of relatively small systems. We illustrate this approach by determining ac , together with the finite size scaling exponent n, for storing Gaussian patterns in committee and p...

Critical percolation in high dimensions: critical exponents, finite size scaling and random walks

Finite-size scaling exponents of the Lipkin-Meshkov-Glick model.

We study the ground state properties of the critical Lipkin-Meshkov-Glick model. Using the Holstein-Primakoff boson representation, and the continuous unitary transformation technique, we compute explicitly the finite-size scaling exponents for the energy gap, the ground state energy, the magnetization, and the spin-spin correlation functions. Finally, we discuss the behavior of the two-spin en...

Critical finite-size scaling with constraints: Fisher renormalization revisited

The influence of a thermodynamic constraint on the critical finite-size scaling behavior of three-dimensional Ising and XY models is analyzed by MonteCarlo simulations. Within the Ising universality class constraints lead to Fisher renormalized critical exponents, which modify the asymptotic form of the scaling arguments of the universal finite-size scaling functions. Within the XY universality...