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 MATRIX FORMULATION OF SUPERSPACE ON 1D LATTICE WITH TWO SUPERCHARGES

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4737-4768 ◽  
Author(s):  
SERGIO ARIANOS ◽  
ALESSANDRO D'ADDA ◽  
ALESSANDRA FEO ◽  
NOBORU KAWAMOTO ◽  
JUN SAITO
Keyword(s):  
Open Problem ◽  
Matrix Representation ◽  
Leibniz Rule ◽  
Supersymmetric Theory ◽  
Tree Level ◽  
Radiative Corrections ◽  
Matrix Formulation ◽  
Ward Identities ◽  
Dimensional Lattice ◽  
One Dimensional

Following the approach developed by some of the authors in recent papers and using a matrix representation for the superfields, we formulate an exact supersymmetric theory with two supercharges on a one-dimensional lattice. In the superfield formalism supersymmetry transformations are uniquely defined and do not suffer of the ambiguities recently pointed out by some authors. The action can be written in a unique way and it is invariant under all supercharges. A modified Leibniz rule applies when supercharges act on a superfield product and the corresponding Ward identities take a modified form but hold exactly at least at the tree level, while their validity in presence of radiative corrections is still an open problem and is not considered here.

scholarly journals Stochastic rumors on random trees

2021 ◽  
Vol 2021 (12) ◽  
pp. 123403
Author(s):  
Valdivino V Junior ◽  
Pablo M Rodriguez ◽  
Adalto Speroto
Keyword(s):  
Phase Transition ◽  
Critical Parameter ◽  
Nearest Neighbor ◽  
Critical Value ◽  
Random Trees ◽  
Discrete Distributions ◽  
Positive Probability ◽  
The Mean

Abstract The Maki–Thompson rumor model is defined by assuming that a population represented by a graph is subdivided into three classes of individuals; namely, ignorants, spreaders and stiflers. A spreader tells the rumor to any of its nearest ignorant neighbors at rate one. At the same rate, a spreader becomes a stifler after a contact with other nearest neighbor spreaders, or stiflers. In this work we study the model on random trees. As usual we define a critical parameter of the model as the critical value around which the rumor either becomes extinct almost-surely or survives with positive probability. We analyze the existence of phase-transition regarding the survival of the rumor, and we obtain estimates for the mean range of the rumor. The applicability of our results is illustrated with examples on random trees generated from some well-known discrete distributions.

The complexity of concatenation on deterministic and alternating finite automata

2018 ◽  
Vol 52 (2-3-4) ◽  
pp. 153-168
Author(s):  
Michal Hospodár ◽  
Galina Jirásková
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Open Problem ◽  
Finite Automata ◽  
The State ◽  
Regular Languages ◽  
Final States ◽  
State Complexity ◽  
Deterministic Automata

We study the state complexity of the concatenation operation on regular languages represented by deterministic and alternating finite automata. For deterministic automata, we show that the upper bound m2n − k2n−1 on the state complexity of concatenation can be met by ternary languages, the first of which is accepted by an m-state DFA with k final states, and the second one by an n-state DFA with ℓ final states for arbitrary integers m, n, k, ℓ with 1 ≤ k ≤ m − 1 and 1 ≤ ℓ ≤ n − 1. In the case of k ≤ m − 2, we are able to provide appropriate binary witnesses. In the case of k = m − 1 and ℓ ≥ 2, we provide a lower bound which is smaller than the upper bound just by one. We use our binary witnesses for concatenation on deterministic automata to describe binary languages meeting the upper bound 2m + n + 1 for the concatenation on alternating finite automata. This solves an open problem stated by Fellah et al. [Int. J. Comput. Math. 35 (1990) 117–132].

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 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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