Majority-Vote Model on Scale-Free Hypergraphs

• Authors: T. Gradowski , A. Krawiecki
• Languages of publication: EN

Abstracts

EN

Majority-vote models on scale-free hypergraphs are investigated by means of numerical simulations with different variants of system dynamics. Hypergraphs are generalisations of ordinary graphs in which higher order of social organisation is included by introducing hyperedges corresponding to social groups, connecting more than two nodes. In the models under study, opinions of agents (two-state spins) placed in nodes are updated according to a probabilistic rule with control parameter representing social noise. The probability of a single spin flip depends on the average opinion within only one social group (hyperedge) the agent belongs to. This introduces an intermediate level of social interactions, in contrast with the case of networks, where the opinion of an agent usually depends on the average opinion of all neighbours. In all cases under consideration a second-order phase transition to a state with an uniform opinion was found as a function of the social noise, with the critical value of the control parameter and the critical exponents depending on the hypergraph topology and details of the system dynamics (node or hyperedge update).

Keywords

EN

89.75.Hc; 64.60.Cn; 05.10.Ln; 05.50.+q; 64.60.F-

Discipline

• 64.60.F-: Equilibrium properties near critical points, critical exponents
• 89.75.Hc: Networks and genealogical trees
• 05.10.Ln: Monte Carlo methods(see also 02.70.Tt, Uu in mathematical methods in physics; for Monte Carlo methods extensively used in subdivisions of physics, see the appropriate section; for example, see 52.65.Pp in plasma simulation)
• 05.50.+q: Lattice theory and statistics (Ising, Potts, etc.)(see also 64.60.Cn Order-disorder transformations, and 75.10.Hk Classical spin models)
• 64.60.Cn: Order-disorder transformations(see also 81.30.Hd Constant-composition solid-solid phase transformations: polymorphic, massive, and order-disorder in materials science; for effects of disorder on superconducting transition temperature, see 74.62.En)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2015
• Volume: 127
• Issue: 3A
• Pages: A-55-A-58

Dates

published

2015-03

Contributors

author

T. Gradowski

• Faculty of Physics, Warsaw University of Technology, Koszykowa 75, PL-00662 Warsaw, Poland

author

A. Krawiecki

• Faculty of Physics, Warsaw University of Technology, Koszykowa 75, PL-00662 Warsaw, Poland

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Identifiers

DOI

10.12693/APhysPolA.127.A-55