scholarly journals Homogeneous Symmetrical Threshold Model with Nonconformity: Independence versus Anticonformity

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Bartłomiej Nowak ◽  
Katarzyna Sznajd-Weron
Keyword(s):  
Phase Transitions ◽  
Complete Graph ◽  
Order Parameter ◽  
Threshold Model ◽  
Majority Vote ◽  
Mean Field ◽  
Exact Result ◽  
Continuous Phase ◽  
Vote Model ◽  
Discontinuous Phase

We study two variants of the modified Watts threshold model with a noise (with nonconformity, in the terminology of social psychology) on a complete graph. Within the first version, a noise is introduced via so-called independence, whereas in the second version anticonformity plays the role of a noise, which destroys the order. The modified Watts threshold model, studied here, is homogeneous and possesses an up-down symmetry, which makes it similar to other binary opinion models with a single-flip dynamics, such as the majority-vote and the q-voter models. Because within the majority-vote model with independence only continuous phase transitions are observed, whereas within the q-voter model with independence also discontinuous phase transitions are possible, we ask the question about the factor, which could be responsible for discontinuity of the order parameter. We investigate the model via the mean-field approach, which gives the exact result in the case of a complete graph, as well as via Monte Carlo simulations. Additionally, we provide a heuristic reasoning, which explains observed phenomena. We show that indeed if the threshold r=0.5, which corresponds to the majority-vote model, an order-disorder transition is continuous. Moreover, results obtained for both versions of the model (one with independence and the second one with anticonformity) give the same results, only rescaled by the factor of 2. However, for r>0.5 the jump of the order parameter and the hysteresis is observed for the model with independence, and both versions of the model give qualitatively different results.

scholarly journals Fundamental ingredients for discontinuous phase transitions in the inertial majority vote model

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Jesus M. Encinas ◽  
Pedro E. Harunari ◽  
M. M. de Oliveira ◽  
Carlos E. Fiore
Keyword(s):  
Phase Transitions ◽  
Majority Vote ◽  
Vote Model ◽  
Discontinuous Phase ◽  
Discontinuous Phase Transitions

scholarly journals Kinetic Models of Discrete Opinion Dynamics on Directed Barabási–Albert Networks

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 942 ◽  
Author(s):  
F. Welington S. Lima ◽  
J. A. Plascak
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Kinetic Models ◽  
Order Parameter ◽  
Majority Vote ◽  
Opinion Dynamics ◽  
Universality Class ◽  
Continuous Phase ◽  
Vote Model ◽  
Continuous Phase Transition

Kinetic models of discrete opinion dynamics are studied on directed Barabási–Albert networks by using extensive Monte Carlo simulations. A continuous phase transition has been found in this system. The critical values of the noise parameter are obtained for several values of the connectivity of these directed networks. In addition, the ratio of the critical exponents of the order parameter and the corresponding susceptibility to the correlation length have also been computed. It is noticed that the kinetic model and the majority-vote model on these directed Barabási–Albert networks are in the same universality class.

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 .

Phase transitions in perovskites near the tricritical point: an experimental study of KMn1–xCaxF3 and SrTiO3

2000 ◽  
Vol 64 (6) ◽  
pp. 971-982 ◽  
Author(s):  
M. C. Gallardo ◽  
F. J. Romero ◽  
S. A. Hayward ◽  
E. K. H. Salje ◽  
J. del Cerro
Keyword(s):  
Experimental Data ◽  
Experimental Study ◽  
Phase Transitions ◽  
Order Parameter ◽  
Tricritical Point ◽  
Mean Field ◽  
Calorimetric Data ◽  
X Ray ◽  
First Order ◽  
Field Behaviour

AbstractWe present experimental data for the Pm3m-I4/mcm phase transitions in the perovskite crystals KMn1-xCaxF3 and SrTiO3. Comparison of calorimetric data (latent heat and specific heat) with order parameter data (measured with X-ray rocking methods) indicates that these transitions follow mean-field behaviour, and may be described using Landau potentials where the free energy expansion includes terms up to Q6. This potential is characteristic of transitions close to the tricritical point. Comparison of the behaviour of SrTiO3 and KMnF3 indicates that KMnF3 is closer to the tricritical point; a small amount of substitution of Ca for Mn causes the transition to cross the tricritical point from first order to second order behaviour.

A MEAN FIELD STUDY OF THE PHASE TRANSITIONS IN A CLASS OF SYSTEMS WITH COMPLEX ORDER PARAMETERS

1994 ◽  
Vol 08 (28) ◽  
pp. 3963-3986
Author(s):  
EVGENIA J. BLAGOEVA
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Order Parameter ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Unconventional Superconductors ◽  
Complex Order ◽  
The Mean ◽  
Expansion Coefficients

A generalized Landau free energy for a complex order parameter expanded up to sixth-order is investigated using group theoretical arguments and the mean-field approximation. Results for the phase transitions that occur are presented. The phase diagram for all allowed values of the expansion coefficients is constructed with an emphasis placed on the influence of the anisotropy in the order parameter space. The results can be used in discussions of unconventional superconductors and modulated structural and magnetic orderings.

scholarly journals Multi-mode excitation drives disorder during the ultrafast melting of a C4-symmetry-broken phase

2022 ◽  
Vol 13 (1) ◽  
Author(s):  
Daniel Perez-Salinas ◽  
Allan S. Johnson ◽  
Dharmalingam Prabhakaran ◽  
Simon Wall
Keyword(s):  
Phase Transitions ◽  
Order Parameter ◽  
Landau Theory ◽  
Mean Field ◽  
Atomic Scale ◽  
Time Dependent ◽  
Ginzburg Landau ◽  
Mode Excitation ◽  
The Mean ◽  
Multi Mode

AbstractSpontaneous C4-symmetry breaking phases are ubiquitous in layered quantum materials, and often compete with other phases such as superconductivity. Preferential suppression of the symmetry broken phases by light has been used to explain non-equilibrium light induced superconductivity, metallicity, and the creation of metastable states. Key to understanding how these phases emerge is understanding how C4 symmetry is restored. A leading approach is based on time-dependent Ginzburg-Landau theory, which explains the coherence response seen in many systems. However, we show that, for the case of the single layered manganite La0.5Sr1.5MnO4, the theory fails. Instead, we find an ultrafast inhomogeneous disordering transition in which the mean-field order parameter no longer reflects the atomic-scale state of the system. Our results suggest that disorder may be common to light-induced phase transitions, and methods beyond the mean-field are necessary for understanding and manipulating photoinduced phases.

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.

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