scholarly journals Critical droplets and phase transitions in two dimensions

2003 ◽  
Vol 67 (1) ◽  
Author(s):  
Santo Fortunato
Keyword(s):  
Phase Transitions ◽  
Two Dimensions ◽  
Critical Droplets

Phase transitions in the six‐state vector Potts model in two dimensions

1984 ◽  
Vol 55 (6) ◽  
pp. 2429-2431 ◽  
Author(s):  
Challa S. S. Murty ◽  
D. P. Landau
Keyword(s):  
Phase Transitions ◽  
Potts Model ◽  
State Vector ◽  
Two Dimensions

INFLUENCE OF DIMENSIONALITY AND SURFACE ORDERING ON PHASE TRANSITIONS: STUDIES OF FREELY-SUSPENDED LIQUID-CRYSTAL FILMS

1994 ◽  
Vol 08 (22) ◽  
pp. 3051-3082 ◽  
Author(s):  
CHRISTIAN BAHR
Keyword(s):  
Phase Transitions ◽  
Liquid Crystal ◽  
Two Dimensions ◽  
Smectic Liquid Crystals ◽  
Liquid Crystal Films ◽  
Integral Number ◽  
Smectic Phases ◽  
Crystal Films ◽  
Freely Suspended ◽  
Freely Suspended Films

Freely-suspended films of smectic liquid crystals can be regarded as membranes consisting of a stack of an integral number of molecular (smectic) layers with the layer planes being parallel to the two free surfaces. Because of their variable thickness (between thousands and only two layers) and the large variety of phase transitions between different smectic phases, freely-suspended films are excellent systems to study the influence of the dimensional cross-over from three to two dimensions on phase transitions. Further, because the free surface of a liquid crystal has a strong ordering effect (contrary to solids which exhibit generally surface-induced disorder), freely-suspended films are well-suited for the study of the effect of enhanced surface order on phase transitions. A review of the corresponding experimental work is given.

scholarly journals Heterotic strings in two dimensions and new stringy phase transitions

2005 ◽  
Vol 2005 (08) ◽  
pp. 035-035 ◽  
Author(s):  
Joshua L Davis ◽  
Finn Larsen ◽  
Nathan Seiberg
Keyword(s):  
Phase Transitions ◽  
Two Dimensions ◽  
Heterotic Strings

Phase transitions in two dimensions

1980 ◽  
Vol 59 (4) ◽  
pp. 375-409 ◽  
Author(s):  
Michael N. Barber
Keyword(s):  
Phase Transitions ◽  
Two Dimensions

scholarly journals Phase transitions of repulsive two-component fermi gases in two dimensions

2021 ◽  
Author(s):  
Martin-Isbjörn Trappe ◽  
Piotr Tadeusz Grochowski ◽  
Jun Hao Hue ◽  
Tomasz Karpiuk ◽  
Kazimierz Rzazewski
Keyword(s):  
Phase Transitions ◽  
Two Dimensions ◽  
Fermi Gases ◽  
Two Component

scholarly journals Monotone Cellular Automata in a Random Environment

2015 ◽  
Vol 24 (4) ◽  
pp. 687-722 ◽  
Author(s):  
BÉLA BOLLOBÁS ◽  
PAUL SMITH ◽  
ANDREW UZZELL
Keyword(s):  
Phase Transitions ◽  
Cellular Automata ◽  
Two Dimensions ◽  
Bootstrap Percolation ◽  
Unified Theory ◽  
Critical Probability ◽  
The Family ◽  
Update Rules ◽  
Critical Class

In this paper we study in complete generality the family of two-state, deterministic, monotone, local, homogeneous cellular automata in $\mathbb{Z}$d with random initial configurations. Formally, we are given a set $\mathcal{U}$ = {X1,. . . , Xm} of finite subsets of $\mathbb{Z}$d \ {0}, and an initial set A0 ⊂ $\mathbb{Z}$d of ‘infected’ sites, which we take to be random according to the product measure with density p. At time t ∈ $\mathbb{N}$, the set of infected sites At is the union of At-1 and the set of all x ∈ $\mathbb{Z}$d such that x + X ∈ At-1 for some X ∈ $\mathcal{U}$. Our model may alternatively be thought of as bootstrap percolation on $\mathbb{Z}$d with arbitrary update rules, and for this reason we call it $\mathcal{U}$-bootstrap percolation.In two dimensions, we give a classification of $\mathcal{U}$-bootstrap percolation models into three classes – supercritical, critical and subcritical – and we prove results about the phase transitions of all models belonging to the first two of these classes. More precisely, we show that the critical probability for percolation on ($\mathbb{Z}$/n$\mathbb{Z}$)2 is (log n)−Θ(1) for all models in the critical class, and that it is n−Θ(1) for all models in the supercritical class.The results in this paper are the first of any kind on bootstrap percolation considered in this level of generality, and in particular they are the first that make no assumptions of symmetry. It is the hope of the authors that this work will initiate a new, unified theory of bootstrap percolation on $\mathbb{Z}$d.

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