Rotational sandpile models: A finite size scaling study
Abstract Nontrivial critical behaviour is observed in equilibrium lattice statistical models under rotational constraint. Effect of rotational constraint on lattice statistical models at out of equilibrium situation is important to study. Critical properties of non-equilibrium steady state of sandpile models are studied under rotational constraint via finite size scaling (FSS) analysis. Not only FSS is found to be valid for a wide range of rotational sandpile models but also they are found to belong to the same universality class.
Multifractal Scaling in the Bak-Tang-Wiesenfeld Sandpile and Edge Events
A widely applicable analysis of numerical data shows that, while the distribution of avalanche areas obeys finite size scaling, that of toppling numbers is universally characterized by a full, nonlinear multifractal spectrum. Boundary effects determine an unusual dependence on system size of the moment scaling exponents of the conditional toppling distribution at a given area. This distribution is also multifractal in the bulk regime. The resulting picture brings to light unsuspected physics of this long-studied prototype model.
SPIRAL BOND ANIMALS - RATIO APPROACH
Bond animals with a constraint of a given winding direction on the square lattice are enumerated up to 14 bonds. Numerical evidence further confirms the previous conjecture using the position space renormalisation group approach, that they belong to a new universality class.