Critical Properties of One Dimensional Mappings

1980 ◽  
pp. 137-154 ◽  
Author(s):  
Bernard Derrida
Keyword(s):  
Critical Properties ◽  
One Dimensional

Pseudo One-Dimensional Ferroelectric Ordering and Critical Properties of CsH2PO4and CsD2PO4

1979 ◽  
Vol 43 (3) ◽  
pp. 231-234 ◽  
Author(s):  
R. Blinc ◽  
B. Žekš ◽  
A. Levstik ◽  
C. Filipič ◽  
J. Slak ◽  
...  
Keyword(s):  
Critical Properties ◽  
One Dimensional

scholarly journals GROWTH OF SURFACES GENERATED BY A PROBABILISTIC CELLULAR AUTOMATION

1999 ◽  
Vol 10 (01) ◽  
pp. 165-181 ◽  
Author(s):  
PRATIP BHATTACHARYYA
Keyword(s):  
Cellular Automaton ◽  
Active Phase ◽  
Deposition Process ◽  
Surface Growth ◽  
Discrete Models ◽  
Critical Properties ◽  
One Dimensional ◽  
Kinetic Roughening ◽  
Evolution Rule ◽  
Roughening Transition

A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in (1+1) dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton which is known to show a transition from an active phase to an absorbing phase at a critical probability associated with two particular components of the evolution rule. In one of these models, called Model A in this paper, the surface growth is defined in terms of the evolving front of the cellular automaton on the space-time plane. In the other model, called Model B, surface growth takes place by a solid-on-solid deposition process controlled by the cellular automaton configurations that appear in successive time-steps. Both the models show a depinning transition at the critical point of the generating cellular automaton. In addition, Model B shows a kinetic roughening transition at this point. The characteristics of the surface width in these models are derived by scaling arguments from the critical properties of the generating cellular automaton and by Monte Carlo simulations.

scholarly journals On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
J. Hutchinson ◽  
J. P. Keating ◽  
F. Mezzadri
Keyword(s):  
Classical System ◽  
Companion Paper ◽  
Quantum Systems ◽  
Spin Systems ◽  
Two Dimensional ◽  
Critical Properties ◽  
One Dimensional ◽  
Classical Systems ◽  
Long Range Interactions ◽  
Quantum Hamiltonian

We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems characterised by long-range interactions and with critical properties equivalent to those of the class of one-dimensional quantum systems treated by the authors in a previous publication. In particular, we use three approaches: the Trotter-Suzuki mapping, the method of coherent states, and a calculation based on commuting the quantum Hamiltonian with the transfer matrix of a classical system. This enables us to establish universality of certain critical phenomena by extension from the results in the companion paper for the classical systems identified.

scholarly journals Transitional Channel Flow: A Minimal Stochastic Model

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1348
Author(s):  
Paul Manneville ◽  
Masaki Shimizu
Keyword(s):  
Laminar Flow ◽  
Stochastic Model ◽  
Channel Flow ◽  
Lateral Spreading ◽  
Critical Properties ◽  
Von Neumann ◽  
One Dimensional ◽  
Longitudinal Splitting ◽  
Thermodynamic Phase ◽  
Single Orientation

In line with Pomeau’s conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes observed in channel flow before its return to laminar flow. Numerical simulations show that a regime with bands obliquely drifting in two stream-wise symmetrical directions bifurcates into an asymmetrical regime, before ultimately decaying to laminar flow. The model is expressed in terms of a probabilistic cellular automaton of evolving von Neumann neighborhoods with probabilities educed from a close examination of simulation results. It implements band propagation and the two main local processes: longitudinal splitting involving bands with the same orientation, and transversal splitting giving birth to a daughter band with an orientation opposite to that of its mother. The ultimate decay stage observed to display one-dimensional DP properties in a two-dimensional geometry is interpreted as resulting from the irrelevance of lateral spreading in the single-orientation regime. The model also reproduces the bifurcation restoring the symmetry upon variation of the probability attached to transversal splitting, which opens the way to a study of the critical properties of that bifurcation, in analogy with thermodynamic phase transitions.

scholarly journals Critical properties of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model in the presence of a uniform field

1996 ◽  
Vol 54 (10) ◽  
pp. 7168-7176 ◽  
Author(s):  
A. Fledderjohann ◽  
C. Gerhardt ◽  
K. H. Mütter ◽  
A. Schmitt ◽  
M. Karbach
Keyword(s):  
Heisenberg Model ◽  
Uniform Field ◽  
Critical Properties ◽  
One Dimensional ◽  
Antiferromagnetic Heisenberg Model ◽  
The One

The Critical Properties of One-Dimensional Extended Hubbard Model

2002 ◽  
Vol 37 (2) ◽  
pp. 237-242
Author(s):  
Wang Zhi-Guo ◽  
Zhang Yu-Mei ◽  
Chen Hong
Keyword(s):  
Hubbard Model ◽  
Critical Properties ◽  
Extended Hubbard Model ◽  
One Dimensional

Critical properties of a one-dimensional frustrated quantum magnetic model

1991 ◽  
Vol 43 (16) ◽  
pp. 13559-13565 ◽  
Author(s):  
P. Sen ◽  
B. K. Chakrabarti
Keyword(s):  
Critical Properties ◽  
One Dimensional ◽  
Magnetic Model
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