Fractal Geometry and Stochastics VI
نویسندگان
چکیده
We provide a review on the physics associated with phase transitions in which continuous scale invariance is broken into discrete invariance. The rich features of this transition characterized by abrupt formation geometric ladder eigenstates, low energy universality without fixed points, anomalies and Berezinskii-Kosterlitz-Thouless scaling described. important role various celebrated single many body quantum systems discussed along recent experimental realizations. Particular focus devoted to realization graphene.
منابع مشابه
Fractal Geometry and Porosity
A fractal is an object or a structure that is self-similar in all length scales. Fractal geometry is an excellent mathematical tool used in the study of irregular geometric objects. The concept of the fractal dimension, D, as a measure of complexity is defined. The concept of fractal geometry is closely linked to scale invariance, and it provides a framework for the analysis of natural phenomen...
متن کاملFacial Beauty and Fractal Geometry
What is it that makes a face beautiful Average faces obtained by photographic or digital blending are judged attractive but not optimally attractive digital exagger ations of deviations from average face blends can lead to higher attractiveness ratings My novel approach to face design however does not involve blending at all Instead the image of a female face with high ratings is composed from ...
متن کاملPercolation fractal exponents without fractal geometry
Classically, percolation critical exponents are linked to the power laws that characterize percolation cluster fractal properties. It is found here that the gradient percolation power laws are conserved even for extreme gradient values for which the frontier of the infinite cluster is no more fractal. In particular the exponent 7/4 which was recently demonstrated to be the exact value for the d...
متن کامل8 . Fractal Geometry
Since Euclid (300 BC) we have been used to perceiving nature with the concept of a threedimensional (3-D) geometry. We measure linear structures in one dimension, area-like structures in two dimensions, and volume-like structures in three dimensions. However, when we measure an object in terms of these three dimensions, we are aware that the geometric model describes a solid body, while a natur...
متن کاملIntroduction to Fractal Geometry
Introduction to Fractal Geometry .................................................................. 1 1. A few Random Quotes ......................................................................... 1 2. Introduction ....................................................................................... 1 3. Types of fractals ........................................................................
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Progress in probability
سال: 2021
ISSN: ['1050-6977', '2297-0428']
DOI: https://doi.org/10.1007/978-3-030-59649-1