The zero temperature quenching dynamics of the ferromagnetic Ising model on a densely connected small world network is studied where long range bonds are added randomly with a finite probability p. We find that in contrast to the sparsely connected networks and random graph, there is no freezing and an initial random configuration of the spins reaches the equilibrium configuration within a very few Monte Carlo time steps in the thermodynamic limit for any p ≠ 0. The residual energy and the number of spins flipped at any time shows an exponential relaxation to equilibrium. The persistence probability is also studied and it shows a saturation within a few time steps, the saturation value being 0.5 in the thermodynamic limit. These results are explained in the light of the topological properties of the network which is highly clustered and has a novel small world behaviour. © EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005.

PARONGAMA SEN

Physics

P K DAS

Fulltext

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

European Physical Journal B

We consider a susceptible-infected-recovered (SIR) epidemic model on a Euclidean network in one dimension in which nodes at a distance l are connected with probability P(l)∝l-δ in addition to nearest neighbors. The topology of the network changes as δ is varied and its effect on the SIR model is studied. R(t), the recovered fraction of population up to time t, and τ, the total duration of the epidemic, are calculated for different values of the infection probabilities q and δ. A threshold behavior is observed for all δ up to δ ≈ 2.0; above the threshold value q = qc, the saturation value Rsat attains a finite value. Both Rsat and τ show scaling behavior in a finite system of size N; and . qc is constant for 0 δ &lt; 1 and increases with δ for 1 &lt; δ ≲ 2. Mean field behavior is seen up to δ ≈ 1.3; weak dependence on δ is observed beyond this value of δ. The distribution of the outbreak sizes is also estimated and found to be unimodal for q &lt; qc and bimodal for q &gt; qc. The results are compared to static percolation phenomena and also to mean field results for finite systems. Discussions on the properties of the Euclidean network are made in the light of the present results. © 2013 IOP Publishing Ltd.

Journal of Physics A: Mathematical and Theoretical

The susceptible-infected-recovered model on a Euclidean network

Randomness is known to affect the dynamical behavior of many systems to a large extent. In this paper we investigate how the nature of randomness affects the dynamics in a zero-temperature quench of the Ising model on two types of random networks. In both networks, which are embedded in a one-dimensional space, the first-neighbor connections exist and the average degree is 4 per node. In random model A the second-neighbor connections are rewired with a probability p, while in random model B additional connections between neighbors at a Euclidean distance l(l&gt;1) are introduced with a probability P(l) lα. We find that for both models, the dynamics leads to freezing such that the system gets locked in a disordered state. The point at which the disorder of the nonequilibrium steady state is maximum is located. The behavior of dynamical quantities such as residual energy, order parameter, and persistence are discussed and compared. Overall, the behavior of physical quantities are similar, although subtle differences are observed due to the difference in the nature of randomness. © 2011 American Physical Society.

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Effect of the nature of randomness on quenching dynamics of the Ising model on complex networks

We consider a one-dimensional Euclidean network which is grown using a preferential attachment. Here the jth incoming node gets attached to the ith existing node with the probability , where lij is the Euclidean distance between them and ki the degree of the ith node. This network is known to have a static phase transition point at . On this network, we employ three different searching strategies based on degrees or distances or both, where the possibility of termination of search chains is allowed. A detailed analysis shows that these strategies are significantly affected by the presence of the static critical point. The distributions of the search path lengths and the success rates are also estimated and compared for the different strategies. These distributions appear to be marginally affected by the static phase transition. © IOP Publishing Ltd.

Journal of Statistical Mechanics: Theory and Experiment

The effect of a static phase transition on searching dynamics

We consider a one-dimensional network in which the nodes at Euclidean distance l can have long range connections with a probabilty [formula presented] in addition to nearest neighbor connections. This system has been shown to exhibit small-world behavior for [formula presented] above which its behavior is like a regular lattice. From the study of the clustering coefficients, we show that there is a transition to a random network at [formula presented] The finite size scaling analysis of the clustering coefficients obtained from numerical simulations indicates that a continuous phase transition occurs at this point. Using these results, we find that the two transitions occurring in this network can be detected in any dimension by the behavior of a single quantity, the average bond length. The phase transitions in all dimensions are nontrivial in nature. © 2002 The American Physical Society.

Journal	Data powered by TypesetEuropean Physical Journal B
Publisher	Data powered by TypesetSPRINGER
ISSN	1434-6028
Open Access	No