Effect of long range connections on an infinite randomness fixed point associated with the quantum phase transitions in a transverse Ising model

Abstract

We study the effect of long-range connections on the infinite-randomness fixed point associated with the quantum phase transitions in a transverse Ising model (TIM). The TIM resides on a long-range connected lattice where any two sites at a distance r are connected with a non-random ferromagnetic bond with a probability that falls algebraically with the distance between the sites as 1/r^{d+σ}. The interplay of the fluctuations due to dilutions together with the quantum fluctuations due to the transverse field leads to an interesting critical behaviour. The exponents at the critical fixed point (which is an infinite randomness fixed point (IRFP)) are related to the classical "long-range" percolation exponents. The most interesting observation is that the gap exponent ψis exactly obtained for all values of σand d. Exponents depend on the range parameter σand show a crossover to short-range values when σ>= 2 -η_{SR} where η_{SR} is the anomalous dimension for the conventional percolation problem. Long-range connections are also found to tune the strength of the Griffiths phase.

5 pages, 1 figure, To appear in Phys. Rev. B

References in corpus (4)

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• Absence of conventional quantum phase transitions in itinerant systems with disorder
• Percolation quantum phase transitions in diluted magnets
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Cited by in corpus (3)

• Strong Disorder RG approach - a short review of recent developments
• Infinite randomness critical behavior of the contact process on networks with long-range connections
• Percolation Transition in a Topological Phase