相关论文: Scaling Relations for Logarithmic Corrections
We study anomalous dimensions of (super)conformal Wilson operators at weak and strong coupling making use of the integrability symmetry on both sides of the gauge/string correspondence and elucidate the origin of their single-logarithmic…
Some general properties of perturbed (rational) CFT in the background metric of symmetric 2D sphere of radius $R$ are discussed, including conformal perturbation theory for the partition function and the large $R$ asymptotic. The truncated…
Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving…
With large-scale Monte Carlo simulations, we confirm that for the two-dimensional XY model, there is a logarithmic correction to scaling in the dynamic relaxation starting from a completely disordered state, while only an inverse power law…
We investigate the location of the critical and tricritical points of the three-dimensional Blume-Capel model by analyzing the behavior of the first Lee-Yang zero, the density of partition function zeros, and higher-order cumulants of the…
We study the zeros of the partition function in the complex temperature plane (Fisher zeros) and in the complex external field plane (Lee-Yang zeros) of a frustrated Ising model with competing nearest-neighbor ($J_1 > 0$) and…
The inaccurate translation of numbers can lead to significant security issues, ranging from financial setbacks to medical inaccuracies. While large language models (LLMs) have made significant advancements in machine translation, their…
Obtaining precise theoretical predictions for both production and decay processes of heavy new particles is of great importance to constrain the allowed parameter spaces of Beyond-the-Standard-Model (BSM) theories, and to properly assess…
This study demonstrates that incorrect data are entered into a pairwise comparisons matrix for processing into weights for the data collected by a rating scale. Unprocessed rating scale data lead to a paradox. A solution to it, based on…
The Cauchy problem for the Yang-Mills system in two space dimensions is treated for data with minimal regularity assumptions. In the classical case of data in $L^2$-based Sobolev spaces we have to assume that the number of derivatives is…
Low-rank approximation is a fundamental technique in modern data analysis, widely utilized across various fields such as signal processing, machine learning, and natural language processing. Despite its ubiquity, the mechanics of low-rank…
Many constructs that characterize language, like its complexity or emotionality, have a naturally continuous semantic structure; a public speech is not just "simple" or "complex," but exists on a continuum between extremes. Although large…
Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique…
The muon optimizer has picked up much attention as of late as a possible replacement to the seemingly omnipresent Adam optimizer. Recently, care has been taken to document the scaling laws of hyper-parameters under muon such as weight decay…
The present review is devoted to the problems of finite-size scaling due to the presence of long-range interaction decaying at large distance as $1/r^{d+\sigma}$, where $d$ is the spatial dimension and the long-range parameter $\sigma>0$.…
Using Finite-Size Scaling techniques we obtain accurate results for critical quantities of the Ising model and the site percolation, in three dimensions. We pay special attention in parameterizing the corrections-to-scaling, what is…
Mathematical reasoning in Large Language Models (LLMs) is often evaluated using benchmarks with limited numerical ranges, failing to reflect real-world problem-solving across diverse scales. Furthermore, most existing evaluation methods…
Scaling laws arise and are eulogized across disciplines from natural to social sciences for providing pithy, quantitative, `scale-free', and `universal' power law relationships between two variables. On a log-log plot, the power laws…
We investigate Lee-Yang zeros of generating functions of dynamical observables and establish a general relation between phase transitions in ensembles of trajectories of stochastic many-body systems and the time evolution of high-order…
The paper describes a generalized iterative proportional fitting procedure which can be used for maximum likelihood estimation in a special class of the general log-linear model. The models in this class, called relational, apply to…