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Long-range connections, quantum magnets and dilute contact processes

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  • Divakaran, Uma
  • Dutta, Amit

Abstract

In this article, we briefly review the critical behaviour of a long-range percolation model in which any two sites are connected with a probability that falls off algebraically with the distance. The results of this percolation transition are used to describe the quantum phase transitions in a dilute transverse Ising model at the percolation threshold pc of the long-range connected lattice. In the similar spirit, we propose a new model of a contact process defined on the same long-range diluted lattice and explore the transitions at pc. The long-range nature of the percolation transition allows us to evaluate some critical exponents exactly in both the above models. Moreover, mean field theory is valid for a wide region of parameter space. In either case, the strength of Griffiths McCoy singularities are tunable as the range parameter is varied.

Suggested Citation

  • Divakaran, Uma & Dutta, Amit, 2007. "Long-range connections, quantum magnets and dilute contact processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(1), pages 39-43.
  • Handle: RePEc:eee:phsmap:v:384:y:2007:i:1:p:39-43
    DOI: 10.1016/j.physa.2007.04.067
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    Cited by:

    1. Di Xiao & Jun Wang & Hongli Niu, 2016. "Volatility Analysis of Financial Agent-Based Market Dynamics from Stochastic Contact System," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 607-625, December.
    2. Ferenc Iglói & Cécile Monthus, 2018. "Strong disorder RG approach – a short review of recent developments," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(11), pages 1-25, November.

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