The phase transition in a one-dimensional lattice of axisymmetric bodies

1987 ◽  
Vol 46 (1-2) ◽  
pp. 67-85 ◽  
Author(s):  
Jerzy Szulga ◽  
Wojbor A. Woyczynski ◽  
Bernard Ycart ◽  
J. Adin Mann
Keyword(s):  
Phase Transition ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Axisymmetric Bodies

scholarly journals AN IMPROVED LOWER BOUND FOR THE CRITICAL PARAMETER OF STAVSKAYA’S PROCESS

2020 ◽  
Vol 102 (3) ◽  
pp. 517-524
Author(s):  
ALEX D. RAMOS ◽  
CALITÉIA S. SOUSA ◽  
PABLO M. RODRIGUEZ ◽  
PAULA CADAVID
Keyword(s):  
Phase Transition ◽  
Lower Bound ◽  
Open Problem ◽  
Critical Parameter ◽  
Critical Value ◽  
The State ◽  
Multicomponent Systems ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Probabilistic Cellular Automaton

We consider Stavskaya’s process, which is a two-state probabilistic cellular automaton defined on a one-dimensional lattice. The state of any vertex depends only on itself and on the state of its right-adjacent neighbour. This process was one of the first multicomponent systems with local interaction for which the existence of a kind of phase transition has been rigorously proved. However, the exact localisation of its critical value remains as an open problem. We provide a new lower bound for the critical value.

scholarly journals Topological phase transition between a normal insulator and a topological metal state in a quasi-one-dimensional system

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Milad Jangjan ◽  
Mir Vahid Hosseini
Keyword(s):  
Phase Transition ◽  
Dimensional System ◽  
Inversion Symmetry ◽  
Topological Phase ◽  
Edge States ◽  
Zero Energy ◽  
One Dimensional ◽  
Topological Phase Transition ◽  
Metal State ◽  
Topological Metal

AbstractWe theoretically report the finding of a new kind of topological phase transition between a normal insulator and a topological metal state where the closing-reopening of bandgap is accompanied by passing the Fermi level through an additional band. The resulting nontrivial topological metal phase is characterized by stable zero-energy localized edge states that exist within the full gapless bulk states. Such states living on a quasi-one-dimensional system with three sublattices per unit cell are protected by hidden inversion symmetry. While other required symmetries such as chiral, particle-hole, or full inversion symmetry are absent in the system.

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