Long-range connections, quantum magnets and dilute contact processes

Divakaran, Uma ; Dutta, Amit (2007) Long-range connections, quantum magnets and dilute contact processes Physica A: Statistical Mechanics and its Applications, 384 (1). pp. 39-43. ISSN 0378-4371

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Official URL: http://doi.org/10.1016/j.physa.2007.04.067

Related URL: http://dx.doi.org/10.1016/j.physa.2007.04.067


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 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 . 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.

Item Type:Article
Source:Copyright of this article belongs to Elsevier B.V.
Keywords:Long-range Percolation; Quantum Magnets; Contact Processes.
ID Code:117214
Deposited On:21 Apr 2021 12:02
Last Modified:21 Apr 2021 12:02

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