Infinite-disorder critical points of models with stretched exponential interactions

Abstract

We show that an interaction decaying as a stretched exponential function of the distance, $J(l)\sim e^{-c{l}^a}$, is able to alter the universality class of short-range systems having an infinite-disorder critical point. To do so, we study the low-energy properties of the random transverse-field Ising chain with the above form of interaction by a strong-disorder renormalization group (SDRG) approach. We obtain that the critical behavior of the model is controlled by infinite-disorder fixed points different from that of the short-range one if $0<a<1/2$. In this range, the critical exponents calculated analytically by a simplified SDRG scheme are found to vary with $a$, while, for $a>1/2$, the model belongs to the same universality class as its short-range variant. The entanglement entropy of a block of size $L$ increases logarithmically with $L$ in the critical point but, as opposed to the short-range model, the prefactor is disorder-dependent in the range $0<a<1/2$. Numerical results obtained by an improved SDRG scheme are found to be in agreement with the analytical predictions. The same fixed points are expected to describe the critical behavior of, among others, the random contact process with stretched exponentially decaying activation rates.

arXiv comment16 pages, 3 figures

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