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 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 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.

Electric and Magnetic Properties of Transition-Metal Carbide Sc3TC4 (T=Co, Ru, Os)

2016 ◽  
Vol 257 ◽  
pp. 34-37
Author(s):  
Takuto Kazama ◽  
Minoru Maeda ◽  
Kouichi Takase ◽  
Yoshiki Takano ◽  
Tadataka Watanabe
Keyword(s):  
Phase Transition ◽  
Magnetic Properties ◽  
Phase Transitions ◽  
Transition Metal ◽  
Density Wave ◽  
Transition Metal Carbide ◽  
Superconducting Transition ◽  
Metal Carbides ◽  
Low Dimensional ◽  
Successive Phase

We investigate electric and magnetic properties of quasi-one-dimensional transition-metal carbides Sc3TC4 (T = Co, Ru, and Os), and their mixed crystals Sc3(Co1-xRux)C4 and Sc3(Ru1-xOsx)C4. Sc3CoC4 exhibits successive phase transitions of charge-density-wave transition at TCDW ~ 140 K, Peierls-like structural transition at Ts ~ 70 K, and superconducting transition at Tc ~ 5 K. Sc3RuC4 and Sc3OsC4 exhibit a phase transition at T* ~ 220 K and 250 K, respectively, which should occur in the low-dimensional electronic structure. For Sc3CoC4, it is revealed by the investigation of the electric and magnetic properties of Sc3(Co1-xRux)C4 that the phase transitions at TCDW, Ts, and Tc exhibit different robustness against Ru doping. For Sc3RuC4 and Sc3OsC4, it is revealed by the investigation of the electric and magnetic properties of Sc3(Ru1-xOsx)C4 that an identical kind of phase transition occurs at T*. Additionally, the present study reveals that the phase transition at T* in Sc3RuC4 and Sc3OsC4 is inherently different from the phase transitions at TCDW, Ts, and Tc in Sc3CoC4.

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.

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.

81Br and 127I NQR and Phase Transitions in CH3NH3 HgBr3 and CH3NH3 HgI3

1990 ◽  
Vol 45 (3-4) ◽  
pp. 343-348 ◽  
Author(s):  
Hiromitsu Terao ◽  
Tsutomu Okuda
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Large Amplitude ◽  
Molecular Motions ◽  
Temperature Variations ◽  
Halogen Atoms ◽  
Resonance Frequencies ◽  
Successive Phase

Abstract The 81Br and 127I NQR spectra were recorded in CH3NH3 HgBr3 and CH3NH HgI3 , respectively. In addition to a phase transition at 338 K, successive phase transitions take place at 127 ± 1, 184±1 and 243±5 K in CH3NH3 HgBr3. On heating, the resonance lines of CH3NH3HgI3 disappear near a phase transition at 328 K and one line appears above this temperature. The temperature variations of the resonance frequencies of the terminal halogen atoms in both crystals are extraordinarily steep. This indicates the large amplitude molecular motions expected for the CH3NH3 cations which are linked to the terminal halogen atoms through N-H ··· X type H-bonding.

Dielectric, pyroelectric, piezoelectric and optical investigation of the phase transition sequence in BaZnGeO4

1994 ◽  
Vol 209 (2) ◽  
Author(s):  
S. Y. Huang ◽  
R. von der Mühll ◽  
J. Ravez ◽  
P. Hagenmuller
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Optical Investigation ◽  
Transition Sequence ◽  
Successive Phase

AbstractThe successive phase transitions of a BaZnGeO

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.

Phase Transitions in 4,4´-Dichlorobenzophenone as Studied by 35Cl FT-NQR

1994 ◽  
Vol 49 (1-2) ◽  
pp. 267-272 ◽  
Author(s):  
Hirokazu Nakayama ◽  
Taro Eguchi ◽  
Nobuo Nakamura
Keyword(s):  
Phase Transition ◽  
Fourier Transform ◽  
Phase Transitions ◽  
Room Temperature ◽  
Thermal Hysteresis ◽  
Thermal Anomaly ◽  
Hysteresis Phenomenon ◽  
Transform Method ◽  
Three Phase ◽  
Successive Phase

Abstract The temperature dependence of 35Cl NQR frequencies in 4,4´-dichlorobenzophenone was measured between 9.3 and 372 K by the pulse Fourier-transform method. Successive phase transitions were observed at 189 and 194 K. Concerning these phase transitions, the curious thermal hysteresis phenomenon found in a previous NQR experiment was not reproduced in the present study. It also follow s that NQR indicates another phase transition around 220 K, although no thermal anomaly was detected there by DTA. Tentative explanations for these three phase transitions are presented in relation to the incommensurability between 189 and 220 K. In addition, a novel phase transition was found to occur at 331 K according to both DTA and 35Cl NQR. A single NQR line observed at room temperature splits into two components above 331 K, suggesting that the symmetry above 331 K is lower than that at room temperature. This is the behavior of re-entrant phase transition, and it reveals the quasi-continuous nature.

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.

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