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Related papers: An exact universal amplitude ratio for percolation

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We consider the scaling behavior of directed percolation and of the pair contact process with a conjugated field. In particular we determine numerically the equation of state and show that both models are characterized by the same universal…

Condensed Matter · Physics 2015-06-24 S. Lubeck , R. D. Willmann

The shape-dependent universality of the excess percolation cluster number and cross-configuration probability on a torus is discussed. Besides the aspect ratio of the torus, the universality class depends upon the twist in the periodic…

Disordered Systems and Neural Networks · Physics 2015-06-25 Robert M. Ziff , Christian D. Lorenz , Peter Kleban

We study the question of universality in the two-dimensional spin-$1$ Baxter-Wu model in the presence of a crystal field $\Delta$. We employ extensive numerical simulations of two types, providing us with complementary results: Wang-Landau…

Statistical Mechanics · Physics 2022-05-26 Alexandros Vasilopoulos , Nikolaos G. Fytas , Erol Vatansever , Anastasios Malakis , Martin Weigel

The two-dimensional Ashkin-Teller model provides the simplest example of a statistical system exhibiting a line of critical points along which the critical exponents vary continously. The scaling limit of both the paramagnetic and…

High Energy Physics - Theory · Physics 2009-11-10 G. Delfino , P. Grinza

Building upon our recent study arXiv:1709.04325, we investigate the feasibility of calculating the pion distribution amplitude from suitably chosen Euclidean correlation functions at large momentum. We demonstrate in this work the advantage…

We propose a method of studying the continuous percolation of aligned objects as a limit of a corresponding discrete model. We show that the convergence of a discrete model to its continuous limit is controlled by a power-law dependency…

Statistical Mechanics · Physics 2016-10-27 Zbigniew Koza , Jakub Poła

A class of $d$-dimensional reaction-diffusion models interpolating continuously between the diffusion-coagulation and the diffusion-annihilation models is introduced. Exact relations among the observables of different models are…

Condensed Matter · Physics 2009-10-28 Daniele Balboni , Pierre-Antoine Rey , Michel Droz

We consider directed percolation processes for particle types A and B coupled unidirectionally by a transmutation reaction A -> B. It is shown that the strong coupling regime of this recently introduced problem defines a universality class…

Soft Condensed Matter · Physics 2007-05-23 R. Dengler

In this work we consider five different lattice models which exhibit continuous phase transitions into absorbing states. By measuring certain universal functions, which characterize the steady state as well as the dynamical scaling…

Statistical Mechanics · Physics 2009-11-11 S. Lubeck , R. D. Willmann

Monte Carlo (MC) and series expansion (SE) data for the energy, specific heat, magnetization and susceptibility of the two-dimensional 4-state Potts model in the vicinity of the critical point are analysed. The role of logarithmic…

Statistical Mechanics · Physics 2008-11-26 Lev Shchur , Bertrand Berche , Paolo Butera

A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…

Statistical Mechanics · Physics 2012-12-11 Stephan Mertens , Cristopher Moore

We argue the exact universal result for the three-point connectivity of critical percolation in two dimensions. Predictions for Potts clusters and for the scaling limit below p_c are also given.

High Energy Physics - Theory · Physics 2014-10-09 Gesualdo Delfino , Jacopo Viti

In a recent paper, we have reported a universal power law for both site and bond percolation thresholds for any lattice of cubic symmetry. Extension to anisotropic lattices is discussed.

Disordered Systems and Neural Networks · Physics 2009-10-30 Serge Galam , Alain Mauger

I consider a one dimensional system of particles which interact through a hard core of diameter $\si$ and can connect to each other if they are closer than a distance $d$. The mean cluster size increases as a function of the density $\rho$…

Statistical Mechanics · Physics 2009-10-28 Alon Drory

We calculate the large-q expansion of the second moment correlation length at the first order phase transition point of the q-state Potts model in two dimensions both in the ordered and disordered phases to order 21 in $1/\sqrt{q}$. They…

High Energy Physics - Lattice · Physics 2007-05-23 H. Arisue

For the fully anisotropic simple-cubic Ising lattice, the critical finite-size scaling amplitudes of both the spin-spin and energy-energy inverse correlation lengths and the singular part of the reduced free-energy density are calculated by…

Condensed Matter · Physics 2009-10-22 M. A. Yurishchev

Percolation theory is usually applied to lattices with a uniform probability p that a site is occupied or that a bond is closed. The more general case, where p is a function of the position x, has received less attention. Previous studies…

Statistical Mechanics · Physics 2012-10-23 Michael T Gastner , Beata Oborny

The harmonic measure (or diffusion field or electrostatic potential) near a percolation cluster in two dimensions is considered. Its moments, summed over the accessible external hull, exhibit a multifractal spectrum, which I calculate…

Statistical Mechanics · Physics 2009-10-31 Bertrand Duplantier

We investigate the quantum percolation problem in a diluted chain with long-range hopping amplitudes. Each bond is activated with probability $p(r) = p_1/r^{\alpha}$, where $r$ is the distance between two sites and $\alpha$ characterizes…

Disordered Systems and Neural Networks · Physics 2009-11-07 Rodrigo P. A. Lima , Marcelo L. Lyra

The finite-size scaling behaviour for percolation and conduction is studied in two-dimensional triangular-shaped random resistor networks at the percolation threshold. The numerical simulations are performed using an efficient star-triangle…

Statistical Mechanics · Physics 2007-05-23 P. Lajko , L. Turban