arXiv subjects

Maciej Wołoszyn

Publications and source records attributed to Maciej Wołoszyn.

13 recordsLinked to original sources

arXiv2026

Heider balance in square versus triangular lattices under an external field

We discuss the Heider model in the presence of an external social field. This field breaks the possible symmetry between the probabilities of hostile and friendly relationships. We consider the system in the presence of fluctuations generated by thermal noise and present the results of a comparative study of two-dimensional triangular and square networks with periodic boundary conditions. The results were obtained using three different methods: exact calculations for small systems ($3 \times 3$ square lattice and $2 \times 2$ triangular lattice), Monte Carlo simulations of medium-sized systems ($16 \times 16$ lattices), and exact calculations in the thermodynamic limit (corresponding to infinite size) of certain limiting cases for which analytical solutions are possible. In particular, we exploit the recently discovered equivalence between structurally balanced systems and the Ising model to derive an exact form of the edge magnetization susceptibility for systems in Heider equilibrium.

cond-mat.stat-mech↗

arXiv2026

Random site percolation with complex neighborhoods in five dimension

In this paper, the random site percolation problem in a five-dimensional space for complex neighborhoods is studied. The efficient C++ code (with ordinary work division) of the classical Newman--Ziff algorithm is presented. The obtained speed-up of computations reduces 2170 years of single-core computations -- necessary for obtaining the results presented in this paper -- much below the typical half-decay time of the scientist. For complex neighborhoods, it is for neighborhoods composed with sites taken from several coordination zones (up to the seventh coordination zone), the 127 percolation thresholds are calculated (with 120 among them being estimated for the first time). For seven extended (compact) neighborhoods, the fractal dimensions are also calculated. The mean value of these fractal dimensions, averaged over these seven compact neighborhoods, is estimated as $\langle d_f\rangle\approx 3.5581(70)$. The percentage errors of the values obtained for the fractal dimensions for compact neighborhoods vary from 0.26\% to 1.76\% with respect to the theoretically predicted value based on scaling relations and the most recent estimates of critical exponents for five-dimensional space. The universality of the percolation threshold as dependent on the weighted coordination number $ζ=\sum_i z_i r_i$ (where $z_i$ is the number of sites in the $i$-th coordination zone and $r_i$ is the Euclidean distance from the sites in the $i$-th coordination zone to the central site) is also verified. The latter manifests itself as the power law ($p_c\proptoζ^{-g}$) with $g\approx 0.7913(43)$

physics.comp-ph↗

arXiv2026

Relationship between Heider links and Ising spins

We show that the Heider model with an external field is equivalent, in the limit of structural balance, to the Ising model with nearest-neighbor interactions without an external field. More precisely, we claim that the signs of the Heider relations that maintain structural equilibrium in the system can be represented as nearest neighbor Ising spin products. We demonstrate this explicitly for a complete graph and provide a general argument for an arbitrary graph. A consequence of the equivalence is that the system of balanced Heider states undergoes a phase transition, inherited from the Ising model, at a critical value of the social field at which the fluctuations of edge magnetization are maximal.

cond-mat.stat-mech↗

arXiv2025

Fine structure of phase diagram for social impact theory

In this paper, the social impact theory introduced by Latané is reconsidered. A fully differentiated society is considered; that is, initially every actor has their own opinion. The equivalent of Muller's ratchet guards that -- even for the non-deterministic case (with a positive social temperature) -- any opinion once removed from the opinion space does not appear again. With computer simulation, we construct the phase diagram for Latané model based on the number of surviving opinions after various evolution times. The phase diagram is constructed on the two-dimensional plane of model control parameters responsible for the effective range of interaction among actors and the social temperature. Introducing the Muller's ratchet-like mechanism gives a non-zero chance for any opinion to be removed from the system. We believe that in such a case, for any positive temperature, ultimately a consensus is reached. However, even for a moderate system size, the time to reach consensus is very long. In contrast, for the deterministic case (without social temperature), the system may be frozen with clusters of actors having several different opinions, or even reach the cycle limit (with blinking structures).

physics.soc-ph↗

arXiv2025

Lower limit of percolation threshold on a square lattice with complex neighborhoods

In this paper, the 60-year-old concept of long-range interaction in percolation problems introduced by Dalton, Domb, and Sykes, is reconsidered. With Monte Carlo simulation -- based on Newman-Ziff algorithm and finite-size scaling hypothesis -- we estimate 64 percolation thresholds for random site percolation problem on a square lattice with neighborhoods that contain sites from the 7th coordination zone. The percolation thresholds obtained range from 0.27013 (for the neighborhood that contains only sites from the 7th coordination zone) to 0.11535 (for the neighborhood that contains all sites from the 1st to the 7th coordination zone). Similarly to neighborhoods with smaller ranges, the power-law dependence of the percolation threshold on the effective coordination number with exponent close to -1/2 is observed. Finally, we empirically determine the limit of the percolation threshold on square lattices with complex neighborhoods. This limit scales with the inverse square of the mean radius of the neighborhood. The boundary of this limit is touched for threshold values associated with extended (compact) neighborhoods.

cond-mat.stat-mech↗

arXiv2025

Heider balance on Archimedean lattices and cliques

We investigate the work function $U(T)$ for the Heider balance, driven by a thermal noise $T$, on several planar networks that contain separated triangles, pairs of triangles, chains of triangles and complex structures of triangles. In simulations, the heat-bath algorithm is applied. Two schemes of link values updating are considered: synchronous and asynchronous (sequential). The latter results are compared with analytical calculations for small cliques. We argue that the actual shape of $U(T)$ is a consequence of a local topology rather than of a macroscopic ordering. Finally, we present the mathematical proof that for any planar lattice, perfect structural (Heider) balance is unreachable at $T>0$.

physics.soc-ph↗

arXiv2024

Universality of opinions disappearing in sociophysical models of opinion dynamics: From initial multitude of opinions to ultimate consensus

Possibility of reaching a consensus in social systems with strong initial fragmentation is one of the most interesting issues in sociopysics. It is also intriguing what the dynamics of such processes is. To address those problems, we performed computer simulations using well-established models of social opinion formation, namely the voter, Sznajd, and Latané models. We investigated opinion dynamics in cases where the initial number of opinions is very large, equal to the number of actors (the voter and Latané models) or when every second actor has their own opinion (Sznajd model), with some variations on the update schemes, lattice topologies, effective ranges of interaction, and information noise levels. For all considered models, the number of opinions assumed by the actors is finally almost always reduced to only one. However, while the voter and Latané models exhibit a power-law time decrease in the number of opinions, the Sznajd model follows a complex three-stage behavior. We also demonstrated that the mean/median time of reaching the consensus scales with system size according to a power law for voter and Sznajd models, while for the Latané model this increase is even faster. Our results show that in the studied models the consensus is possible, provided that a long enough and model-dependent time to reach this state is available.

physics.soc-ph↗

arXiv2023

Thermal properties of structurally balanced systems on classical random graphs

The dynamics of social relations and the possibility of reaching the state of structural balance (Heider balance) under the influence of the temperature modeling the social noise level are discussed for interacting actors occupying nodes of classical random graphs. Depending on the graph density $D$, either a smooth cross-over or a first-order phase transition from a balanced to an imbalanced state of the system is observed with an increase of the thermal noise level. The minimal graph density $D_\text{min}$ for which the first-order phase transition can be observed decreases with system size $N$ as $D_\text{min}\propto N^{-0.58(1)}$. For graph densities $D>D_\text{min}$ the reduced critical temperature $T_c^\star=T_c/T_c(D=1)$ increases with the graph density as $T_c^\star\propto D^{1.719(6)}$ independently of the system size $N$.

physics.soc-ph↗

arXiv2022

Status achieved in an organization -- rank dynamics

A new model of an evolution of ranks of employees due to staff turnover in an organization is designed. If the rank is determined only by the performance, the rank shift of incumbents due to the turnover is proportional to the initial rank: the status of high staff is reduced only slightly. This effect that has been observed in the literature. However, if the status also depends on some other variable, the positions of high staff may be greatly deteriorated. In that case, the effect depends nonlinearly on the time $τ$ between subsequent replacements of staff.

physics.soc-ph↗

arXiv2022

Thermal properties of structurally balanced systems on diluted and densified triangulations

The dynamics of social relations and the possibility of reaching the state of structural balance (Heider balance) are discussed for various networks of interacting actors under the influence of the temperature modeling the social noise level. For that purpose, two main types of lattices are considered. The first is created by removing some links from a regular triangular lattice to produce a diluted triangular lattice, and the second by adding more links to create an enhanced triangular lattice. In both those cases, the full range of possible graph densities is discussed, limited by the extreme cases of networks which consist of a small number of separated triads and fully connected networks. It is shown that the existence of the balanced state is not possible if the average node degree is too close to the value characterizing the regular triangular lattice. Otherwise, both balanced (or partially balanced) and imbalanced states are possible, depending on the temperature. However, only for graphs which are dense enough a phase transition of the first kind is observed, while less enhanced networks (and all diluted) indicate a smooth cross-over between the two states. The cross-over temperatures are size-independent only for the diluted triangular lattices and depend on the size of the system for the enhanced triangular lattices, as is the case also for the critical temperatures of the phase transition observed in denser enhanced lattices.

physics.soc-ph↗

arXiv2020

Expulsion from structurally balanced paradise

We perform simulations of structural balance evolution on a triangular lattice using the heat-bath algorithm. In contrast to similar approaches---but applied to analysis of complete graphs---the triangular lattice topology successfully prevents the occurrence of even partial Heider balance. Starting with the state of Heider's paradise, it is just a matter of time when the evolution of the system leads to an unbalanced and disordered state. The time of the system relaxation does not depend on the system size. The lack of any signs of a balanced state was not observed in earlier investigated systems dealing with the structural balance.

physics.soc-ph↗

arXiv2020

Towards the Heider balance with a cellular automaton

The state of structural balance (termed also `Heider balance') of a social network is often discussed in social psychology and sociophysics. In this state, actors at network nodes classify other individuals as enemies or friends. Hence, the network contains two kinds of links: positive and negative. Here a new cellular automaton is designed and investigated, which mimics the time evolution towards the structural balance. The automaton is deterministic and synchronous. The medium is the triangular lattice with some fraction $f$ of links removed. We analyse the number of unbalanced triads (parameterized as `energy'), the frequencies of balanced triads and correlations between them. The time evolution enhances the local correlations of balanced triads. Local configurations of unbalanced triads are found which are blinking with period of two time steps.

physics.soc-ph↗

arXiv2016

Transition from positive to negative magnetoresistance induced by a constriction in semiconductor nanowire

We have studied the magnetotransport through an indium antimonide (InSb) nanowire grown in [111] direction, with a geometric constriction and in an external magnetic field applied along the nanowire axis. We have found that the magnetoresistance is negative for the narrow constriction, nearly zero for the constriction of some intermediate radius, and takes on positive values for the constriction with the radius approaching that of the nanowire. For all magnitudes of the magnetic field, the radius of constriction at which the change of the magnetoresistance sign takes place has been found to be almost the same as long as other geometric parameters of the nanowire are fixed. The sign reversing of the magnetoresistance is explained as a combined effect of two factors: the influence of the constriction on the transverse states and the spin Zeeman effect.

cond-mat.mes-hall↗