Criticality in diluted ferromagnets

Agliari, Elena; Barra, Adriano; Camboni, Federico

doi:10.1088/1742-5468/2008/10/p10003

Cited by 24 publications

(61 citation statements)

References 36 publications

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“…When J > 0 interacting units tend to "imitate" each other. In this ferromagnetic context one can prove that the bipartite topology does not induce any qualitative effects: results are the same (under a proper rescaling) as for the Curie Weiss model; indeed, in this case one can think of bipartition as a particular dilution on the previous fully-connected scheme and we know that (pathological cases apart), dilution does not affect the physical scenario [35][36][37][38]. Differently from low-dimensional systems such as the linear Ising-chains, the Curie-Weiss model admits sharp (eventually discontinuous in the thermodynamic limit) transitions from an empty ( m A = m B = 0) to a completely filled ( m A = m B = 1) configuration as the field h is tuned.…”

Section: The Cooperative Case: Chemical Kineticsmentioning

confidence: 55%

Collective behaviours: from biochemical kinetics to electronic circuits

Agliari

Barra

Burioni

et al. 2013

Sci Rep

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In this work we aim to highlight a close analogy between cooperative behaviors in chemical kinetics and cybernetics; this is realized by using a common language for their description, that is mean-field statistical mechanics. First, we perform a one-to-one mapping between paradigmatic behaviors in chemical kinetics (i.e., non-cooperative, cooperative, ultra-sensitive, anti-cooperative) and in mean-field statistical mechanics (i.e., paramagnetic, high and low temperature ferromagnetic, anti-ferromagnetic). Interestingly, the statistical mechanics approach allows a unified, broad theory for all scenarios and, in particular, Michaelis-Menten, Hill and Adair equations are consistently recovered. This framework is then tested against experimental biological data with an overall excellent agreement. One step forward, we consistently read the whole mapping from a cybernetic perspective, highlighting deep structural analogies between the above-mentioned kinetics and fundamental bricks in electronics (i.e. operational amplifiers, flashes, flip-flops), so to build a clear bridge linking biochemical kinetics and cybernetics.

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Section: The Cooperative Case: Chemical Kineticsmentioning

confidence: 55%

Collective behaviours: from biochemical kinetics to electronic circuits

Agliari

Barra

Burioni

et al. 2013

Sci Rep

Self Cite

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show abstract

“…First, we notice that, the average values stemming from both routes are comparable within the related errors. Moreover, the second route turns out to be more noisy; this result perfectly matches with the fact that, in a Monte Carlo-like simulation, means computed on different graph are less accurate than the ones related to a single realization of network (see e.g., [38]). Anyhow, the numerical path followed in Sec.…”

Section: Appendix B -Technical Details On Numerical Simulationssupporting

confidence: 72%

Phase Transition for the Maki–Thompson Rumour Model on a Small-World Network

et al. 2017

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We consider the Maki-Thompson model for the stochastic propagation of a rumour within a population. We extend the original hypothesis of homogenously mixed population by allowing for a small-world network embedding the model. This structure is realized starting from a k-regular ring and by inserting, in the average, c additional links in such a way that k and c are tuneable parameter for the population architecture. We prove that this system exhibits a transition between regimes of localization (where the final number of stiflers is at most logarithmic in the population size) and propagation (where the final number of stiflers grows algebraically with the population size) at a finite value of the network parameter c. A quantitative estimate for the critical value of c is obtained via extensive numerical simulations.

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“…Such random structures, typically modeled by Erdös-Rény (ER) graphs, have attracted a great deal of interest in the last years also due to new tools introduced for their investigation (see e.g. [16,17]).…”

Section: Introductionmentioning

confidence: 99%

Trapping of continuous-time quantum walks on Erdös–Rényi graphs

Agliari

2011

Physica A: Statistical Mechanics and its Applications

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We consider the coherent exciton transport, modeled by continuous-time quantum walks, on Erdös-Rény graphs in the presence of a random distribution of traps. The role of trap concentration and of the substrate dilution is deepened showing that, at long times and for intermediate degree of dilution, the survival probability typically decays exponentially with a (average) decay rate which depends non monotonically on the graph connectivity; when the degree of dilution is either very low or very high, stationary states, not affected by traps, get more likely giving rise to a survival probability decaying to a finite value. Both these features constitute a qualitative difference with respect to the behavior found for classical walks.

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Criticality in diluted ferromagnets

Cited by 24 publications

References 36 publications

Collective behaviours: from biochemical kinetics to electronic circuits

Collective behaviours: from biochemical kinetics to electronic circuits

Phase Transition for the Maki–Thompson Rumour Model on a Small-World Network

Trapping of continuous-time quantum walks on Erdös–Rényi graphs

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