scholarly journals Is Independence Necessary for a Discontinuous Phase Transition within the q-Voter Model?

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 521 ◽  
Author(s):  
Angelika Abramiuk ◽  
Jakub Pawłowski ◽  
Katarzyna Sznajd-Weron
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Continuous Phase ◽  
Voter Model ◽  
Social Response ◽  
Generalized Model ◽  
Independent Variables ◽  
The Social ◽  
Discontinuous Phase ◽  
Independent Behavior

We ask a question about the possibility of a discontinuous phase transition and the related social hysteresis within the q-voter model with anticonformity. Previously, it was claimed that within the q-voter model the social hysteresis can emerge only because of an independent behavior, and for the model with anticonformity only continuous phase transitions are possible. However, this claim was derived from the model, in which the size of the influence group needed for the conformity was the same as the size of the group needed for the anticonformity. Here, we abandon this assumption on the equality of two types of social response and introduce the generalized model, in which the size of the influence group needed for the conformity q c and the size of the influence group needed for the anticonformity q a are independent variables and in general q c ≠ q a . We investigate the model on the complete graph, similarly as it was done for the original q-voter model with anticonformity, and we show that such a generalized model displays both types of phase transitions depending on parameters q c and q a .

scholarly journals A Veritable Zoology of Successive Phase Transitions in the Asymmetric q-Voter Model on Multiplex Networks

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1018
Author(s):  
Anna Chmiel ◽  
Julian Sienkiewicz ◽  
Agata Fronczak ◽  
Piotr Fronczak
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Continuous Phase ◽  
Voter Model ◽  
Complete Graphs ◽  
Opinion Formation ◽  
Multiplex Networks ◽  
Multiplex Network ◽  
Two Parameters ◽  
Successive Phase

We analyze a nonlinear q-voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. The size of the lobby q (i.e., the pressure group) is a crucial parameter that changes the behavior of the system. The q-voter model has been applied on multiplex networks, and it has been shown that the character of the phase transition depends on the number of levels in the multiplex network as well as on the value of q. The primary aim of this study is to examine phase transition character in the case when on each level of the network the lobby size is different, resulting in two parameters q1 and q2. In a system of a duplex clique (i.e., two fully overlapped complete graphs) we find evidence of successive phase transitions when a continuous phase transition is followed by a discontinuous one or two consecutive discontinuous phase transitions appear, depending on the parameter. When analyzing this system, we even encounter mixed-order (or hybrid) phase transition. The observation of successive phase transitions is a new quantity in binary state opinion formation models and we show that our analytical considerations are fully supported by Monte-Carlo simulations.

scholarly journals Explosive Percolation in Erdős–Rényi-Like Random Graph Processes

2012 ◽  
Vol 22 (1) ◽  
pp. 133-145 ◽  
Author(s):  
KONSTANTINOS PANAGIOTOU ◽  
RETO SPÖHEL ◽  
ANGELIKA STEGER ◽  
HENNING THOMAS
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Random Graph ◽  
Continuous Phase ◽  
Selection Rules ◽  
Continuous Phase Transition ◽  
Empty Graph ◽  
Numerical Evidence ◽  
Discontinuous Phase ◽  
Discontinuous Phase Transitions

The study of the phase transition of random graph processes, and recently in particular Achlioptas processes, has attracted much attention. Achlioptas, D'Souza and Spencer (Science, 2009) gave strong numerical evidence that a variety of edge-selection rules in Achlioptas processes exhibit a discontinuous phase transition. However, Riordan and Warnke (Science, 2011) recently showed that all these processes have a continuous phase transition.In this work we prove discontinuous phase transitions for three random graph processes: all three start with the empty graph on n vertices and, depending on the process, we connect in every step (i) one vertex chosen randomly from all vertices and one chosen randomly from a restricted set of vertices, (ii) two components chosen randomly from the set of all components, or (iii) a randomly chosen vertex and a randomly chosen component.

Percolation phase transition of static and growing networks under a weighted function

2016 ◽  
Vol 27 (07) ◽  
pp. 1650082 ◽  
Author(s):  
Xiao Jia ◽  
Jin-Song Hong ◽  
Ya-Chun Gao ◽  
Hong-Chun Yang ◽  
Chun Yang ◽  
...  
Keyword(s):  
Phase Transition ◽  
Continuous Phase ◽  
Weighted Function ◽  
Percolation Process ◽  
Practical Applications ◽  
Network Intervention ◽  
Growing Networks ◽  
Discontinuous Phase ◽  
And Control ◽  
Growing Network

We investigate the percolation phase transitions in both the static and growing networks where the nodes are sampled according to a weighted function with a tunable parameter [Formula: see text]. For the static network, i.e. the number of nodes is constant during the percolation process, the percolation phase transition can evolve from continuous to discontinuous as the value of [Formula: see text] is tuned. Based on the properties of the weighted function, three typical values of [Formula: see text] are analyzed. The model becomes the classical Erdös–Rényi (ER) network model at [Formula: see text]. When [Formula: see text], it is shown that the percolation process generates a weakly discontinuous phase transition where the order parameter exhibits an extremely abrupt transition with a significant jump in large but finite system. For [Formula: see text], the cluster size distribution at the lower pseudo-transition point does not obey the power-law behavior, indicating a strongly discontinuous phase transition. In the case of growing network, in which the collection of nodes is increasing, a smoother continuous phase transition emerges at [Formula: see text], in contrast to the weakly discontinuous phase transition of the static network. At [Formula: see text], on the other hand, probability modulation effect shows that the nature of strongly discontinuous phase transition remains the same with the static network despite the node arrival even in the thermodynamic limit. These percolation properties of the growing networks could provide useful reference for network intervention and control in practical applications in consideration of the increasing size of most actual networks.

scholarly journals Generalized Independence in the q-Voter Model: How Do Parameters Influence the Phase Transition?

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 120 ◽  
Author(s):  
Angelika Abramiuk ◽  
Katarzyna Sznajd-Weron
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Broad Spectrum ◽  
Order Parameter ◽  
Analytical Formula ◽  
Voter Model ◽  
Pair Approximation ◽  
Scaling Relation ◽  
Independent Behavior

We study the q-voter model with flexibility, which allows for describing a broad spectrum of independence from zealots, inflexibility, or stubbornness through noisy voters to self-anticonformity. Analyzing the model within the pair approximation allows us to derive the analytical formula for the critical point, below which an ordered (agreement) phase is stable. We determine the role of flexibility, which can be understood as an amount of variability associated with an independent behavior, as well as the role of the average network degree in shaping the character of the phase transition. We check the existence of the scaling relation, which previously was derived for the Sznajd model. We show that the scaling is universal, in a sense that it does not depend neither on the size of the group of influence nor on the average network degree. Analyzing the model in terms of the rescaled parameter, we determine the critical point, the jump of the order parameter, as well as the width of the hysteresis as a function of the average network degree ⟨ k ⟩ and the size of the group of influence q.

scholarly journals Topological Frustration can modify the nature of a Quantum Phase Transition

2021 ◽  
Author(s):  
Vanja Marić ◽  
Gianpaolo Torre ◽  
Fabio Franchini ◽  
Salvatore Giampaolo
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Quantum Phase Transition ◽  
Landau Theory ◽  
Continuous Phase ◽  
Quantum Systems ◽  
Quantum Phase ◽  
Local Order ◽  
Ginzburg Landau ◽  
One Dimensional

Abstract Ginzburg-Landau theory of continuous phase transitions implicitly assumes that microscopic changes are negligible in determining the thermodynamic properties of the system. In this work we provide an example that clearly contrasts with this assumption. In particular, we consider the 2-cluster-Ising model, a one-dimensional spin-1/2 system that is known to exhibit a quantum phase transition between a magnetic and a nematic phase. By imposing boundary conditions that induce topological frustration we show that local order is completely destroyed on both sides of the transition and that the two thermodynamic phases can only be characterized by string order parameters. Having proved that topological frustration is capable of altering the nature of a system's phase transition, this result is a clear challenge to current theories of phase transitions in complex quantum systems.

scholarly journals Continuous phase transitions on Galton–Watson trees

2021 ◽  
pp. 1-31
Author(s):  
Tobias Johnson
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Discrete Systems ◽  
Continuous Phase ◽  
Recursive Structure ◽  
Continuous Phase Transition ◽  
First Order ◽  
First Order Phase Transition ◽  
The Mean ◽  
First Order Phase

Abstract Distinguishing between continuous and first-order phase transitions is a major challenge in random discrete systems. We study the topic for events with recursive structure on Galton–Watson trees. For example, let $\mathcal{T}_1$ be the event that a Galton–Watson tree is infinite and let $\mathcal{T}_2$ be the event that it contains an infinite binary tree starting from its root. These events satisfy similar recursive properties: $\mathcal{T}_1$ holds if and only if $\mathcal{T}_1$ holds for at least one of the trees initiated by children of the root, and $\mathcal{T}_2$ holds if and only if $\mathcal{T}_2$ holds for at least two of these trees. The probability of $\mathcal{T}_1$ has a continuous phase transition, increasing from 0 when the mean of the child distribution increases above 1. On the other hand, the probability of $\mathcal{T}_2$ has a first-order phase transition, jumping discontinuously to a non-zero value at criticality. Given the recursive property satisfied by the event, we describe the critical child distributions where a continuous phase transition takes place. In many cases, we also characterise the event undergoing the phase transition.

scholarly journals Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bartłomiej Nowak ◽  
Bartosz Stoń ◽  
Katarzyna Sznajd-Weron
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Complete Graph ◽  
Opinion Dynamics ◽  
Voter Model ◽  
Quenched Disorder ◽  
Popular Opinion ◽  
Discontinuous Phase ◽  
Dynamics Models ◽  
Discontinuous Phase Transitions

AbstractWe introduce a generalized version of the noisy q-voter model, one of the most popular opinion dynamics models, in which voters can be in one of $$s \ge 2$$ s ≥ 2 states. As in the original binary q-voter model, which corresponds to $$s=2$$ s = 2 , at each update randomly selected voter can conform to its q randomly chosen neighbors only if they are all in the same state. Additionally, a voter can act independently, taking a randomly chosen state, which introduces disorder to the system. We consider two types of disorder: (1) annealed, which means that each voter can act independently with probability p and with complementary probability $$1-p$$ 1 - p conform to others, and (2) quenched, which means that there is a fraction p of all voters, which are permanently independent and the rest of them are conformists. We analyze the model on the complete graph analytically and via Monte Carlo simulations. We show that for the number of states $$s>2$$ s > 2 the model displays discontinuous phase transitions for any $$q>1$$ q > 1 , on contrary to the model with binary opinions, in which discontinuous phase transitions are observed only for $$q>5$$ q > 5 . Moreover, unlike the case of $$s=2$$ s = 2 , for $$s>2$$ s > 2 discontinuous phase transitions survive under the quenched disorder, although they are less sharp than under the annealed one.

Characterizing multiple continuous phase transitions at an alloying anode with voltammetric measurements and first-principles calculations

2019 ◽  
Vol 7 (40) ◽  
pp. 23121-23129 ◽  
Author(s):  
Yong-Seok Choi ◽  
Jae-Chul Lee
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
First Principles ◽  
Continuous Phase ◽  
First Principles Calculations ◽  
Continuous Phase Transition ◽  
Voltammetric Measurement ◽  
Voltammetric Measurements

In this study, a combination of first-principles calculations and voltammetric measurement is used to identify multiple and continuous phase transition behaviors at the Sb anode during the Na–Sb battery cycles.

scholarly journals Understanding the Influence of Measurement Uncertainty on the Atmospheric Transition in Rainfall and Column Water Vapor

2015 ◽  
Vol 72 (5) ◽  
pp. 2041-2054 ◽  
Author(s):  
James B. Gilmore
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Water Vapor ◽  
Measurement Uncertainty ◽  
Rain Rate ◽  
Tropical Rainfall Measuring Mission ◽  
Continuous Phase ◽  
Large Variability ◽  
Continuous Phase Transition ◽  
Rain Rates

Abstract Measurement uncertainty plays a key role in understanding physical relationships. This is particularly the case near phase transitions where order parameters undergo fast changes and display large variability. Here the proposed atmospheric continuous phase transition is examined by analyzing uncertainty in rain-rate and column water vapor measurements from the Tropical Rainfall Measuring Mission and through an idealized error analysis. It is shown through both of these approaches that microwave rain-rate retrievals can mimic a continuous phase transition. This occurs because microwave retrievals of instantaneous rain rates have a suppressed range. This work also suggests that column water vapor noise may provide part of the plateau seen in the observational relationship. Using updated measurements, this work indicates that the atmosphere is unlikely to undergo a continuous phase transition in rain rate but, instead, contains much larger variability in rain rates at extreme column water vapor values than previously thought. This implies that the atmosphere transitions from a low-variance nonraining state to a high-variance raining state at extreme column water vapor values.

scholarly journals MULTI-HOP GENERALIZED CORE PERCOLATION ON COMPLEX NETWORKS

2020 ◽  
Vol 23 (01) ◽  
pp. 2050001 ◽  
Author(s):  
YILUN SHANG
Keyword(s):  
Phase Transition ◽  
Complex Networks ◽  
Heterogeneous Networks ◽  
Large Scale ◽  
Real Life ◽  
Continuous Phase ◽  
Global Vision ◽  
Discontinuous Phase ◽  
Analytical Frameworks ◽  
Selection Of

Recent theoretical studies on network robustness have focused primarily on attacks by random selection and global vision, but numerous real-life networks suffer from proximity-based breakdown. Here we introduce the multi-hop generalized core percolation on complex networks, where nodes with degree less than [Formula: see text] and their neighbors within [Formula: see text]-hop distance are removed progressively from the network. The resulting subgraph is referred to as [Formula: see text]-core, extending the recently proposed [Formula: see text]-core and classical core of a network. We develop analytical frameworks based upon generating function formalism and rate equation method, showing for instance continuous phase transition for [Formula: see text]-core and discontinuous phase transition for [Formula: see text]-core with any other combination of [Formula: see text] and [Formula: see text]. We test our theoretical results on synthetic homogeneous and heterogeneous networks, as well as on a selection of large-scale real-world networks. This unravels, e.g., a unique crossover phenomenon rooted in heterogeneous networks, which raises a caution that endeavor to promote network-level robustness could backfire when multi-hop tracing is involved.

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