Related papers: Block scaling in the directed percolation universa…
In the field of freezing colloidal suspensions, it is important to understand the particle-scale behavior of particle packing. Here, we reveal the dynamics of particle packing by identifying the behavior of each single particle in situ. The…
Diffusion-limited aggregation is consistent with simple scaling. However, strong subdominant terms are present, and these can account for various earlier claims of anomalous scaling. We show this in detail for the case of multiscaling.
The finite-size scaling function of the magnetization of the ferromagnetic Heisenberg chain is argued to be universal with respect to the magnitude of the spin. The finite-size scaling function is given explicitly by an analytical…
Driven suspensions, where energy is input at a particle scale, are a framework for understanding general principles of out-of-equilibrium organization. A large number of simple interacting units can give rise to non-trivial structure and…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
The properties of the absorbing states of non-equilibrium models belonging to the conserved directed percolation universality class are studied. We find that at the critical point the absorbing states are hyperuniform, exhibiting…
The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources. Yet, while empirically validated, its theoretical underpinnings remain poorly…
Intermediate energy scale physics plays a very important role in non-equilibrium dynamics of quasi-low dimensional cold atom systems. In this article we obtain the universal scaling relations for the generalized reflection coefficient,…
Universality, where microscopic details become irrelevant, takes place in thermodynamic phase transitions. The universality is captured by a singular scaling function of the thermodynamic variables, where the scaling exponents are…
Jammed packings' mechanical properties depend sensitively on their detailed local structure. Here we provide a complete characterization of the pair correlation close to contact and of the force distribution of jammed frictionless spheres.…
The transport properties of disordered systems are known to depend critically on dimensionality. We study the diffusion coefficient of a quantum particle confined to a lattice on the surface of a tube, where it scales between the 1D and 2D…
The effect of an electric field on conduction in a disordered system is an old but largely unsolved problem. Experiments cover an wide variety of systems - amorphous/doped semiconductors, conducting polymers, organic crystals, manganites,…
Absorbing phase transition in restricted exclusion processes are characterized by simple integer exponents. We show that this critical behaviour flows to the directed percolation (DP) universality class when particle conservation is broken…
We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple…
We investigate scaling phenomena at first-order quantum transitions, when the boundary conditions favor one of the two phases. We show that the corresponding finite-size scaling behavior, arising from the interplay between the driving…
We study the large-$r$ behavior of the bulk order-parameter correlation function $G(\bf{r})$ for $T>T_c$ within the lattice $\phi^4$ theory. We also study the large-$L$ behavior of the susceptibility $\chi$ of the confined lattice system of…
We define a percolation problem on the basis of spin configurations of the two dimensional XY model. Neighboring spins belong to the same percolation cluster if their orientations differ less than a certain threshold called the conducting…
The multifractal analysis of disorder induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly distributed observables at…
The problem of the interplay between normal and anomalous scaling in turbulent systems stirred by a random forcing with a power law spectrum is addressed. We consider both linear and nonlinear systems. As for the linear case, we study…
A previous scaling analysis of pressure experiments in heavy fermion is reviewed and enlarged. We show that the critical exponents obtained from this analysis indicate that a one-parameter scaling describes these experiments. We obtain…