7,353 research outputs found
Socio-economical dynamics as a solvable spin system on co-evolving networks
We consider social systems in which agents are not only characterized by
their states but also have the freedom to choose their interaction partners to
maximize their utility. We map such systems onto an Ising model in which spins
are dynamically coupled by links in a dynamical network. In this model there
are two dynamical quantities which arrange towards a minimum energy state in
the canonical framework: the spins, s_i, and the adjacency matrix elements,
c_{ij}. The model is exactly solvable because microcanonical partition
functions reduce to products of binomial factors as a direct consequence of the
c_{ij} minimizing energy. We solve the system for finite sizes and for the two
possible thermodynamic limits and discuss the phase diagrams.Comment: 5 pages 3 fig
Boolean decision problems with competing interactions on scale-free networks: Critical thermodynamics
We study the critical behavior of Boolean variables on scale-free networks
with competing interactions (Ising spin glasses). Our analytical results for
the disorder-network-decay-exponent phase diagram are verified using Monte
Carlo simulations. When the probability of positive (ferromagnetic) and
negative (antiferromagnetic) interactions is the same, the system undergoes a
finite-temperature spin-glass transition if the exponent that describes the
decay of the interaction degree in the scale-free graph is strictly larger than
3. However, when the exponent is equal to or less than 3, a spin-glass phase is
stable for all temperatures. The robustness of both the ferromagnetic and
spin-glass phases suggests that Boolean decision problems on scale-free
networks are quite stable to local perturbations. Finally, we show that for a
given decay exponent spin glasses on scale-free networks seem to obey
universality. Furthermore, when the decay exponent of the interaction degree is
larger than 4 in the spin-glass sector, the universality class is the same as
for the mean-field Sherrington-Kirkpatrick Ising spin glass.Comment: 14 pages, lots of figures and 2 table
Dynamic rewiring in small world networks
We investigate equilibrium properties of small world networks, in which both
connectivity and spin variables are dynamic, using replicated transfer matrices
within the replica symmetric approximation. Population dynamics techniques
allow us to examine order parameters of our system at total equilibrium,
probing both spin- and graph-statistics. Of these, interestingly, the degree
distribution is found to acquire a Poisson-like form (both within and outside
the ordered phase). Comparison with Glauber simulations confirms our results
satisfactorily.Comment: 21 pages, 5 figure
Agent Based Models of Language Competition: Macroscopic descriptions and Order-Disorder transitions
We investigate the dynamics of two agent based models of language
competition. In the first model, each individual can be in one of two possible
states, either using language or language , while the second model
incorporates a third state XY, representing individuals that use both languages
(bilinguals). We analyze the models on complex networks and two-dimensional
square lattices by analytical and numerical methods, and show that they exhibit
a transition from one-language dominance to language coexistence. We find that
the coexistence of languages is more difficult to maintain in the Bilinguals
model, where the presence of bilinguals in use facilitates the ultimate
dominance of one of the two languages. A stability analysis reveals that the
coexistence is more unlikely to happen in poorly-connected than in fully
connected networks, and that the dominance of only one language is enhanced as
the connectivity decreases. This dominance effect is even stronger in a
two-dimensional space, where domain coarsening tends to drive the system
towards language consensus.Comment: 30 pages, 11 figure
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