Universal Scaling Functions for Numbers of Percolating Clusters on Planar Lattices

1996 ◽  
Vol 77 (1) ◽  
pp. 8-11 ◽  
Author(s):  
Chin-Kun Hu ◽  
Chai-Yu Lin
Keyword(s):  
Scaling Functions ◽  
Universal Scaling ◽  
Planar Lattices

Universal scaling functions of a dissipative Manna model

2011 ◽  
Vol 182 (1) ◽  
pp. 226-228 ◽  
Author(s):  
Chien-Fu Chen ◽  
An-Chung Cheng ◽  
Yi-Duen Wang ◽  
Chai-Yu Lin
Keyword(s):  
Scaling Functions ◽  
Universal Scaling

scholarly journals Universal scaling in active single-file dynamics

Soft Matter ◽  
2020 ◽  
Vol 16 (30) ◽  
pp. 7077-7087 ◽  
Author(s):  
Pritha Dolai ◽  
Arghya Das ◽  
Anupam Kundu ◽  
Chandan Dasgupta ◽  
Abhishek Dhar ◽  
...  
Keyword(s):  
Size Distribution ◽  
Cluster Size ◽  
Cluster Size Distribution ◽  
Scaling Functions ◽  
Tagged Particle ◽  
Universal Scaling ◽  
Active Particles ◽  
Single File

The single-file dynamics of various models of interacting scalar active particles shows universality. The cluster size distribution and tagged-particle MSD scale with density and activity parameters with the same scaling functions across all models.

scholarly journals UNIVERSAL SCALING BEHAVIOR OF NON-EQUILIBRIUM PHASE TRANSITIONS

2004 ◽  
Vol 18 (31n32) ◽  
pp. 3977-4118 ◽  
Author(s):  
SVEN LÜBECK
Keyword(s):  
Renormalization Group ◽  
Phase Transitions ◽  
Critical Phenomena ◽  
Equilibrium Phase ◽  
Finite Size ◽  
Universality Class ◽  
Scaling Functions ◽  
Universal Scaling ◽  
Universality Classes ◽  
Non Equilibrium

Non-equilibrium critical phenomena have attracted a lot of research interest in the recent decades. Similar to equilibrium critical phenomena, the concept of universality remains the major tool to order the great variety of non-equilibrium phase transitions systematically. All systems belonging to a given universality class share the same set of critical exponents, and certain scaling functions become identical near the critical point. It is known that the scaling functions vary more widely between different universality classes than the exponents. Thus, universal scaling functions offer a sensitive and accurate test for a system's universality class. On the other hand, universal scaling functions demonstrate the robustness of a given universality class impressively. Unfortunately, most studies focus on the determination of the critical exponents, neglecting the universal scaling functions. In this work a particular class of non-equilibrium critical phenomena is considered, the so-called absorbing phase transitions. Absorbing phase transitions are expected to occur in physical, chemical as well as biological systems, and a detailed introduction is presented. The universal scaling behavior of two different universality classes is analyzed in detail, namely the directed percolation and the Manna universality class. Especially, directed percolation is the most common universality class of absorbing phase transitions. The presented picture gallery of universal scaling functions includes steady state, dynamical as well as finite size scaling functions. In particular, the effect of an external field conjugated to the order parameter is investigated. Incorporating the conjugated field, it is possible to determine the equation of state, the susceptibility, and to perform a modified finite-size scaling analysis appropriate for absorbing phase transitions. Focusing on these equations, the obtained results can be applied to other non-equilibrium continuous phase transitions observed in numerical simulations or experiments. Thus, we think that the presented picture gallery of universal scaling functions is valuable for future work. Additionally to the manifestation of universality classes, universal scaling functions are useful in order to check renormalization group results quantitatively. Since the renormalization group theory is the basis of our understanding of critical phenomena, it is of fundamental interest to examine the accuracy of the obtained results. Due to the continuing improvement of computer hardware, accurate numerical data have become available, resulting in a fruitful interplay between numerical investigations and renormalization group analyzes.

Universal Scaling Functions in Critical Phenomena

1995 ◽  
Vol 75 (14) ◽  
pp. 2786-2786 ◽  
Author(s):  
Chin-Kun Hu ◽  
Chai-Yu Lin ◽  
Jau-Ann Chen
Keyword(s):  
Critical Phenomena ◽  
Scaling Functions ◽  
Universal Scaling

scholarly journals COMPARATIVE STUDY OF SPANNING CLUSTER DISTRIBUTIONS IN DIFFERENT DIMENSIONS

1999 ◽  
Vol 10 (04) ◽  
pp. 747-752 ◽  
Author(s):  
PARONGAMA SEN
Keyword(s):  
Comparative Study ◽  
Percolation Threshold ◽  
Power Law ◽  
Probability Distributions ◽  
Scaling Functions ◽  
Universal Scaling ◽  
Simple Power ◽  
Different Dimensions ◽  
The Masses

The probability distributions of the masses of the clusters spanning from top to bottom of a percolating lattice at the percolation threshold are obtained in all dimensions, from two to five. The first two cumulants and the exponents for the universal scaling functions are shown to have simple power law variations with the dimensionality. The cases where multiple spanning clusters occur are discussed separately and compared.

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