arXiv subjects

Bartłomiej Nowak

Publications and source records attributed to Bartłomiej Nowak.

6 recordsLinked to original sources

arXiv2022

Switching from a continuous to discontinuous phase transition under the quenched disorder

Discontinuous phase transitions occurs to be particularly interesting from a social point of view because of their relationship to social hysteresis and critical mass. In this paper, we show that the replacement of a time-varying (annealed, situation-based) disorder by a static (quenched, personality-based) one can lead to a change from a continuous to a discontinuous phase transition. This is a result beyond the state of art, because so far numerous studies on various complex systems (physical, biological and social) have indicated that the quenched disorder can round or destroy the existence of a discontinuous phase transition. To show the possibility of the opposite behavior, we study a multistate $q$-voter model, with two types of disorder related to random competing interactions (conformity and anticonformity). We confirm, both analytically and through Monte Carlo simulations, that indeed discontinuous phase transitions can be induced by a static disorder.

physics.soc-ph↗

arXiv2022

The threshold model with anticonformity under random sequential updating

We study an asymmetric version of the threshold model with anticonformity under asynchronous update mode that mimics continuous time. We study this model on a complete graph using three different approaches: mean-field approximation, Monte Carlo simulation, and the Markov chain approach. The latter approach yields analytical results for arbitrarily small systems, in contrast to the mean-field approach, which is strictly correct only for an infinite system. We show that for sufficiently large systems, all three approaches produce the same results, as expected. We consider two cases: (1) homogeneous, in which all agents have the same tolerance threshold, and (2) heterogeneous, in which the thresholds are given by a beta distribution parametrized by two positive shape parameters $α$ and $β$. The heterogeneous case can be treated as a generalized model that reduces to a homogeneous model in special cases. We show that particularly interesting behaviors, including social hysteresis and critical mass, arise only for values of $α$ and $β$ that yield the shape of the distribution observed in real social systems.

physics.soc-ph↗

arXiv2021

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

We 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 $s \ge 2$ states. As in the original binary $q$-voter model, which corresponds to $s=2$, at each update randomly selected voter can conform to its $q$ randomly chosen neighbors (copy their state) only if all $q$ neighbors are 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 $1-p$ 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 $s>2$ model displays discontinuous phase transitions for any $q>1$, on contrary to the model with binary opinions, in which discontinuous phase transitions are observed only for $q>5$. Moreover, unlike the case of $s=2$, for $s>2$ discontinuous phase transitions survive under the quenched disorder, although they are less sharp than under the annealed one.

physics.soc-ph↗

arXiv2020

Competing local and global interactions in social dynamics: how important is the friendship network?

Motivated by the empirical study that identifies a correlation between particular social responses and different interaction ranges, we study the $q$-voter model with various combinations of local and global sources of conformity and anticonformity. The models are investigated by means of the pair approximation and Monte Carlo simulations on Watts-Strogatz and Barabási-Albert networks. We show that within the model with local conformity and global anticonformity, the agreement in the system is the most difficult to achieve, and the role of the network structure is the most significant. Interestingly, the model with swapped interaction ranges, namely with global conformity and local anticonformity, becomes almost insensitive to the changes in the network structure. The obtained results may have far reaching consequences for marketing strategies conducted via social media channels.

physics.soc-ph↗

arXiv2020

In search for the social hysteresis -- the symmetrical threshold model with independence on Watts-Strogatz graphs

We study the homogeneous symmetrical threshold model with independence (noise) by pair approximation and Monte Carlo simulations on Watts-Strogatz graphs. The model is a modified version of the famous Granovetter's threshold model: with probability $p$ a voter acts independently, i.e. takes randomly one of two states +/-; with complementary probability $1-p$, a voter takes a given state, if sufficiently large fraction (above a given threshold r) of individuals in its neighborhood is in this state. We show that the character of the phase transition, induced by the noise parameter p, depends on the threshold r, as well as graph's parameters. For r=0.5 only continuous phase transitions are observed, whereas for r>0.5 also discontinuous phase transitions are possible. The hysteresis increases with the average degree and the rewriting parameter beta. On the other hand, the dependence between the width of the hysteresis and the threshold $r$ is non-monotonic. The value of r, for which the maximum hysteresis is observed, overlaps pretty well the size of the majority used for the descriptive norms in order to manipulate people within social experiments. We put results obtained within this paper in a broader picture and discuss them in the context of two other models of binary opinions, namely the majority-vote and the q-voter model.

physics.soc-ph↗

arXiv2019

Homogeneous symmetrical threshold model with nonconformity: independence vs. anticonformity

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 posses 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.

physics.soc-ph↗