相关论文: Finite-size effects in roughness distribution scal…

We study the standard three-dimensional driven diffusive system on a simple cubic lattice where particle jumps along a given lattice direction are biased by an infinitely strong field, while those along other directions follow the usual…

Recently, the concept of geometric renormalization group provides a good approach for studying the structural symmetry and functional invariance of complex networks. Along this line, we systematically investigate the finite-size scaling of…

Finite-size scaling at fixed renormalization-group invariant is a powerful and flexible technique to analyze Monte Carlo data at a critical point. It consists in fixing a given renormalization-group invariant quantity to a given value,…

According to the concept of typicality, an ensemble average can be accurately approximated by an expectation value with respect to a single pure state drawn at random from a high-dimensional Hilbert space. This random-vector approximation,…

Recent advances in foundation models have led to a promising trend of developing large recommendation models to leverage vast amounts of available data. Still, mainstream models remain embarrassingly small in size and na\"ive enlarging does…

Pinning models are built from discrete renewal sequences by rewarding (or penalizing) the trajectories according to their number of renewal epochs up to time $N$, and $N$ is then sent to infinity. They are statistical mechanics models to…

We consider discrete models of kinetic rough interfaces that exhibit space-time scale-invariance in height-height correlation. A generic scaling theory implies that the dynamical structure factor of the height profile can uniquely…

Local porosity distributions for a three-dimensional porous medium and local porosity distributions for a two-dimensional plane-section through the medium are generally different. However, for homogeneous and isotropic media having finite…

Weights initialization in deep neural networks have a strong impact on the speed of converge of the learning map. Recent studies have shown that in the case of random initializations, a chaos/order phase transition occur in the space of…

We analytically derive, in the context of the replica formalism, the first finite size corrections to the average optimal cost in the random assignment problem for a quite generic distribution law for the costs. We show that, when moving…

The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/f^alpha noise signals is studied. Our starting point is the generalization of the model of Gaussian, time-periodic, 1/f noise, discussed in our…

Scaling and hyperscaling laws provide exact relations among critical exponents describing the behavior of a system at criticality. For nonequilibrium growth models with a conserved drift there exist few of them. One such relation is $\alpha…

Open cellular solids usually possess random microstructures that may contain a characteristic length scale, such as the cell size. This gives rise to size dependent mechanical properties where large systems behave differently from small…

Finite size scaling is a powerful tool to study the critical properties of systems governed by one relevant operator, assuming all irrelevant operators have scaling dimensions much smaller then zero. This condition is likely not satisfied…

We introduce and validate a finite-size two-body excess entropy integral equation. By using analytical arguments and computer simulations of prototypical simple liquids, we show that the excess entropy $s_2$ exhibits a finite-size scaling…

We introduce four new real-world distribution shift datasets consisting of changes in image style, image blurriness, geographic location, camera operation, and more. With our new datasets, we take stock of previously proposed methods for…

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…

We study discrete KPZ growth models deposited on square lattice substrates, whose (average) lateral size enlarges as $L= L_0 + \omega t^{\gamma}$. Our numerical simulations reveal that the competition between the substrate expansion and the…

To construct continuum stochastic growth equations for competitive nonequilibrium surface-growth processes of the type RD+X that mixes random deposition (RD) with a correlated-growth process X, we use a simplex decomposition of the height…

We analyze the shapes of roughness distributions of discrete models in the Kardar, Parisi and Zhang (KPZ) and in the Villain, Lai and Das Sarma (VLDS) classes of interface growth, in one and two dimensions. Three KPZ models in d=2 confirm…