Related papers: Finite-size analysis in neural network classificat…
We investigate the connection between the supervised learning of the binary phase classification in the ferromagnetic Ising model and the standard finite-size-scaling theory of the second-order phase transition. Proposing a minimal…
Machine learning has been successfully applied to identify phases and phase transitions in condensed matter systems. However, quantitative characterization of the critical fluctuations near phase transitions is lacking. In this study we…
The order parameter for a continuous transition shows diverging fluctuation near the critical point. Here we show, through numerical simulations and scaling arguments, that the inequality (or variability) between the values of an order…
The Ising model on a $restricted$ scale-free network (SFN) has been studied employing Monte Carlo simulations. This network is described by a power-law degree distribution in the form $P(k)~k^{-\alpha}$, and is called restricted, because…
Determining the universality class of a system exhibiting critical phenomena is one of the central problems in physics. There are several methods to determine this universality class from data. As methods performing collapse plots onto…
The main question raised in the article is whether a neural network trained on a spin lattice model in one universality class can be used to test a model in another universality class. The quantities of interest are the critical phase…
In this work we present a thorough analysis of the phase transitions that occur in a ferromagnetic 2D Ising model, with only nearest-neighbors interactions, in the framework of the Tsallis nonextensive statistics. We performed Monte Carlo…
Finite-size scaling (FSS) for a critical phase transition ($t=0$) states that within a window of size $|t|\sim L^{-1/\nu}$, the scaling behavior of any observable $Q$ in a system of linear size $L$ asymptotically follows a scaling form as…
We discuss the finite-size scaling of the ferromagnetic Ising model on random regular graphs. These graphs are locally tree-like, and in the limit of large graphs, the Bethe approximation gives the exact free energy per site. In the…
We study the critical behavior of the Ising model in annealed scale-free (SF) networks of finite system size with forced upper cutoff in degree. By mapping the model onto the weighted fully connected Ising model, we derive analytic results…
It was recently shown [Phys. Rev. Lett. {\bf 110}, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming…
It is shown by Monte Carlo method that the finite size scaling (FSS) holds in the two dimensional random-coupled Ising ferromagnet. It is also demonstrated that the form of universal FSS function constructed via novel FSS scheme depends on…
The correlation length plays a pivotal role in finite-size scaling and hyperscaling at continuous phase transitions. Below the upper critical dimension, where the correlation length is proportional to the system length, both finite-size…
Using tensor network methods, we perform finite-size scaling analysis to study the parameter-induced phase transitions of two-dimensional deformed Affleck-Kennedy-Lieb-Tasaki states. We use higher-order tensor renormalization group method…
The onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated. Using a mean-field approximation, we characterize sample-to-sample fluctuations for networks of finite size, and…
Finite-size scaling at fixed renormalization-group invariant is a powerful and flexible technique to analyze Monte Carlo data at a critical point. It consists in fixing a given renormalization-group invariant quantity to a given value,…
For small training set sizes $P$, the generalization error of wide neural networks is well-approximated by the error of an infinite width neural network (NN), either in the kernel or mean-field/feature-learning regime. However, after a…
A finite-size-scaling (FSS) theory is proposed for various models in complex networks. In particular, we focus on the FSS exponent, which plays a crucial role in analyzing numerical data for finite-size systems. Based on the…
Based on the isospin-dependent quantum molecular dynamics model, finite-size scaling effects on nuclear liquid--gas phase transition probes are investigated by studying the de-excitation processes of six thermal sources of different sizes…
The disorder-driven phase transition of the RFIM is observed using exact ground-state computer simulations for hyper cubic lattices in d=5,6,7 dimensions. Finite-size scaling analyses are used to calculate the critical point and the…