Related Experiment Video
Updated: May 26, 2026

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
Published on: June 15, 2022
Critical behavior of the Ising model on random fractals
1Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Denis Diderot-Paris 7, Paris, France.
Abstract:
We study the critical behavior of the Ising model in the case of quenched disorder constrained by fractality on random Sierpinski fractals with a Hausdorff dimension d(f) is approximately equal to 1.8928. This is a first attempt to study a situation between the borderline cases of deterministic self-similarity and quenched randomness. Intensive Monte Carlo simulations were carried out. Scaling corrections are much weaker than in the deterministic cases, so that our results enable us to ensure that finite-size scaling holds, and that the critical behavior is described by a new universality class. The hyperscaling relation is compatible with an effective dimension equal to the Hausdorff one; moreover the two eigenvalues exponents of the renormalization flows are shown to be different from the ones calculated from ε expansions, and from the ones obtained for fourfold symmetric deterministic fractals. Although the space dimensionality is not integer, lack of self-averaging properties exhibits some features very close to the ones of a random fixed point associated with a relevant disorder.
More Related Videos
Related Concept Videos
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The Entropy as a State Function
Entropy and the Second Law of Thermodynamics
Random Error
Random Variables
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
Entropy

