Related papers: Finite- Size Scaling of Correlation Function
We give an intuitive geometric explanation for the apparent breakdown of standard finite-size scaling in systems with periodic boundaries above the upper critical dimension. The Ising model and self-avoiding walk are simulated on…
The power of matrix product states to describe infinite-size translational-invariant critical spin chains is investigated. At criticality, the accuracy with which they describe ground state properties of a system is limited by the size…
Collective behaviour in biological systems is often accompanied by strong correlations. The question has therefore arisen of whether correlation is amplified by the vicinity to some critical point in the parameters space. Biological…
For systems with infinite-order phase transitions, in which an order parameter smoothly becomes nonzero, a new observable for finite-size scaling analysis is suggested. By construction this new observable has the favourable property of…
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…
We study the two-point correlation function in the model of branched polymers and its relation to the critical behaviour of the model. We show that the correlation function has a universal scaling form in the generic phase with the only…
We study two different versions of the site-diluted Ising model in three dimensions with long-range spatially correlated disorder by Monte Carlo means. We use finite-size scaling techniques to compute the critical exponents of these…
For finite random systems, it is possible to define two types of variances (noises). It is demonstrated that their ratio is useful in calculating the correlation length of an infinite and rather general random system, as a function of…
We address the question of weak versus strong universality scenarios for the random-bond Ising model in two dimensions. A finite-size scaling theory is proposed, which explicitly incorporates $\ln L$ corrections ($L$ is the linear finite…
We study the scaling properties of critical particle systems confined by a potential. Using renormalization-group arguments, we show that their critical behavior can be cast in the form of a trap-size scaling, resembling finite-size scaling…
Critical point scaling in a field $H$ applies for the limits $t\to 0$, (where $t=T/T_c-1$) and $H\to 0$ but with the ratio $R=t/H^{2/\Delta}$ finite. $\Delta$ is a critical exponent of the zero-field transition. We study the replicon…
We simulated the fourier transform of the correlation function of the Ising model in two and three dimensions using a single cluster algorithm with improved estimators. The simulations are in agreement with series expansion and the…
We study long-range correlation functions of the rectangular Ising lattice with cyclic boundary conditions. Specifically, we consider the situation in which two spins are on the same column, and at least one spin is on or near free…
We present a new method for the calculation of fragment size correlations in a discrete finite system in which correlations explicitly due to the finite extent of the system are suppressed. To this end, we introduce a combinatorial model,…
The two-dimensional Ising model with Brascamp-Kunz boundary conditions has a partition function more amenable to analysis than its counterpart on a torus. This fact is exploited to exactly determine the full finite-size scaling behaviour of…
We present a finite-size scaling analysis of high-statistics Monte Carlo simulations of the three-dimensional randomly site-diluted and bond-diluted Ising model. The critical behavior of these systems is affected by slowly-decaying scaling…
The corrections to finite-size scaling in the critical two-point correlation function G(r) of 2D Ising model on a square lattice have been studied numerically by means of exact transfer-matrix algorithms. The systems of square geometry with…
We study the finite-size behavior of two-dimensional spin-glass models. We consider the +-J model for two different values of the probability of the antiferromagnetic bonds and the model with Gaussian distributed couplings. The analysis of…
The search for the QCD critical end point (CEP) is a major objective of contemporary heavy-ion physics, motivating the study of fluctuation observables that are sensitive to critical dynamics. In particular, baryon-number fluctuations…
Statistical systems near a classical critical point have been intensively studied both from theoretical and experimental points of view. In particular, correlation functions are of relevance in comparing theoretical models with the…