Related papers: Finite-size scaling theory for explosive percolati…
The aim of this paper is to test numerically the predictions of the Mode Coupling Theory (MCT) of the glass transition and study its finite size scaling properties in a model with an exact MCT transition, which we choose to be the fully…
The hyperscaling relation and standard finite-size scaling (FSS) are known to break down above the upper critical dimension due to dangerous irrelevant variables. We establish a coherent formalism for FSS at quantum phase transitions above…
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 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 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…
We analyze large deviations of the time-averaged activity in the one dimensional Fredrickson-Andersen model, both numerically and analytically. The model exhibits a dynamical phase transition, which appears as a singularity in the large…
In the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of statistical physics models. They are well understood at a…
Based on quasi-stationary distribution ideas, a general finite size scaling theory is proposed for discontinuous nonequilibrium phase transitions into absorbing states. Analogously to the equilibrium case, we show that quantities such as,…
Networks are ubiquitous in diverse real-world systems. Many empirical networks grow as the number of nodes increases with time. Percolation transitions in growing random networks can be of infinite order. However, when the growth of large…
We show numerically that correlation length at the critical point in the five-dimensional Ising model varies with system size L as L^{5/4}, rather than proportional to L as in standard finite size scaling (FSS) theory. Our results confirm a…
A quantum tricritical point is shown to exists in coupled time-reversal symmetry (TRS) broken Majorana chains. The tricriticality separates topologically ordered, symmetry protected topological (SPT), and trivial phases of the system. Here…
The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is…
To understand the finite-size-scaling properties of phases transitions in classical and quantum models in the presence of quenched disorder, it has proven to be fruitful to introduce the notion of a finite-size-pseudo-critical point in each…
For the two dimensional classical XY model we present extensive high -temperature -phase bulk data extracted based on a novel finite size scaling (FSS) Monte Carlo technique, along with FSS data near criticality. Our data verify that…
We analyze numerically three different models exhibiting an absorbing phase transition. We focus on the finite-size scaling as well as the dynamical scaling behavior. An accurate determination of several critical exponents allows to…
We study the out-of-equilibrium behavior of statistical systems along critical relaxational flows arising from instantaneous quenches of the temperature $T$ to the critical point $T_c$, starting from equilibrium conditions at time $t=0$. In…
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 expressions for the current near the continuous phase transition, and for the local density near the first-order transition, are found in the steady state of the one-dimensional fully asymmetric simple-exclusion process…
Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…
The evolution of the largest component has been studied intensely in a variety of random graph processes, starting in 1960 with the Erd\"os-R\'enyi process. It is well known that this process undergoes a phase transition at n/2 edges when,…