Related papers: Finite size scaling for homogeneous pinning models
First order quantum phase transitions (1QPTs) are signaled, in the thermodynamic limit, by discontinuous changes in the ground state properties. These discontinuities affect expectation values of observables, including spatial correlations.…
In the finite-size scaling analysis of Monte Carlo data, instead of computing the observables at fixed Hamiltonian parameters, one may choose to keep a renormalization-group invariant quantity, also called phenomenological coupling, fixed…
We address the problem of the definition of the finite-volume correlation length. First, we study the large-N limit of the N-vector model, and we show the existence of several constraints on the definition if regularity of the finite-size…
Finite-size scaling (FSS) is a standard technique for measuring scaling exponents in spin glasses. Here we present a critique of this approach, emphasizing the need for all length scales to be large compared to microscopic scales. In…
Finite-size scaling above the upper critical dimension is a long-standing puzzle in the field of Statistical Physics. Even for pure systems various scaling theories have been suggested, partially corroborated by numerical simulations. In…
We have investigated the random walk problem in a finite system and studied the crossover induced in the the persistence probability scales by the system size.Analytical and numerical work show that the scaling function is an exponentially…
In this paper, we propose several models, which can realize synchronization of complex networks in finite time effectively. The results apply to heterogeneous dynamic networks, too. The mechanism of finite time convergence is revealed.…
Linked cluster expansions are generalized from an infinite to a finite volume on a $d$-dimensional hypercubic lattice. They are performed to 20th order in the expansion parameter to investigate the phase structure of scalar $O(N)$ models…
Pin sequences play an important role in the structural study of permutation classes. In this paper, we study the permutation classes that comprise all the finite subpermutations contained in an infinite pin sequence. We prove that these…
The kinetic equations describing irreversible aggregation and the scaling approach developed to describe them in the limit of large times and large sizes are tersely reviewed. Next, a system is considered in which aggregates can only react…
Controlling complex networks is of paramount importance in science and engineering. Despite recent efforts to improve controllability and synchronous strength, little attention has been paid to the speed of pinning synchronizability (rate…
We consider a random field $\varphi:\{1,...,N\}\to \mathbb{R}$ with Laplacian interaction of the form $\sum_iV(\Delta\varphi_i)$, where $\Delta$ is the discrete Laplacian and the potential $V(\cdot)$ is symmetric and uniformly strictly…
We consider models of directed random polymers interacting with a defect line, which are known to undergo a pinning/depinning (or localization/delocalization) phase transition. We are interested in critical properties and we prove, in…
A binary liquid near its consolute point exhibits critical fluctuations of the local composition; the diverging correlation length has always challenged simulations. The method of choice for the calculation of critical points in the phase…
Neural scaling laws define a predictable relationship between a model's parameter count and its performance after training in the form of a power law. However, most research to date has not explicitly investigated whether scaling laws can…
We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character…
The percolation threshold for flow or conduction through voids surrounding randomly placed spheres is rigorously calculated. With large scale Monte Carlo simulations, we give a rigorous continuum treatment to the geometry of the…
Critical finite-size scaling functions for the order parameter distribution of the two and three dimensional Ising model are investigated. Within a recently introduced classification theory of phase transitions, the universal part of the…
The critical behavior of the stochastic susceptible-infected-recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered…
The use of machine learning models in system identification has increased due to their ability to approximate complex nonlinear dynamics with high accuracy. However, often it is not clear how the performance of trained models scales with…