Related papers: Finite-size scaling theory for explosive percolati…
We calculate universal finite size scaling functions for the order parameter and the longitudinal susceptibility of the three-dimensional O(4) model. The phase transition of this model is supposed to be in the same universality class as the…
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…
Quantum transport through devices coupled to electron reservoirs can be described in terms of the full counting statistics (FCS) of charge transfer. Transport observables, such as conductance and shot-noise power are just cumulants of FCS…
The Ising model in two dimensions with the special boundary conditions of Brascamp and Kunz is analysed. Leading and sub-dominant scaling behaviour of the Fisher zeroes are determined exactly. The finite-size scaling, with corrections, of…
The application of an external field often renders empirical criteria for identifying liquid-gas phase transitions ambiguous. Here, we demonstrate that the finite-size scaling of the density profile provides a definitive criterion to…
We study the scaling properties of Higgs-Yukawa models. Using the technique of Finite-Size Scaling, we are able to derive scaling functions that describe the observables of the model in the vicinity of a Gaussian fixed point. A feasibility…
The universal behaviour of the directed percolation universality class is well understood, both the critical scaling as well as finite size scaling. This article focuses on the block (finite size) scaling of the order parameter and its…
We study the percolation transition in growing networks under an Achlioptas process (AP). At each time step, a node is added in the network and, with the probability $\delta$, a link is formed between two nodes chosen by an AP. We find that…
We study the first-passage time (FPT) problem for widespread recurrent processes in confined though large systems and present a comprehensive framework for characterizing the FPT distribution over many time scales. We find that the FPT…
The scaling of the number of Rydberg excitations in a laser-driven cloud of atoms with the interaction strength is found to be affected by the finite size of the system. The scaling predicted by a theoretical model is compared with results…
An improved version of the Olami-Feder-Christensen model has been introduced to consider avalanche size differences. Our model well demonstrates the power-law behavior and finite size scaling of avalanche size distribution in any range of…
We present the finite-size scaling theory of one-dimensional quantum critical systems in the presence of boundaries. While the finite-size spectrum in the conformal limit, namely of a conformal field theory with conformally invariant…
By using the maximum entropy principle with Tsallis entropy we obtain a fragment size distribution function which undergoes a transition to scaling. This distribution function reduces to those obtained by other authors using Shannon…
Machine learning-inspired techniques have emerged as a new paradigm for analysis of phase transitions in quantum matter. In this work, we introduce a supervised learning algorithm for studying critical phenomena from measurement data, which…
The finite-size scaling function of the nonlinear susceptibility of the ferromagnetic Heisenberg chain is given explicitly. It is conjectured that the scaling function is universal for any values of $S$. The conjecture is based on the exact…
It is proposed that the $O(n)$ spin and geometrical percolation models can help to study the QCD phase diagram due to the universality properties of the phase transition. In this paper, correlations and fluctuations of various sizes of…
A d-dimensional finite quantum model system confined to a general hypercubical geometry with linear spatial size L and ``temporal size'' 1/T (T - temperature of the system) is considered in the spherical approximation under periodic…
Thermal and magnetic effects in a system consisting of thin layers of coupled Ising spins with $S=1/2$ and $S=1$ are considered. The specific heat and the correlation length display maxima at two different temperatures. It is discussed in…
We discuss a scaling theory of the lattice response in the vicinity of a finite-temperature critical end point. The thermal expansivity is shown to be more singular than the specific heat such that the Gr\"uneisen ratio diverges as the…
The emergence of large-scale connectivity and synchronization are crucial to the structure, function and failure of many complex socio-technical networks. Thus, there is great interest in analyzing phase transitions to large-scale…