Cluster geometry and survival probability in systems driven by reaction–diffusion dynamics

Windus, Alastair

doi:10.1088/1367-2630/10/11/113023

Cited by 5 publications

(8 citation statements)

References 17 publications

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“…When p > p c , the long-range interaction is irrelevant. The other variant is the so-called tricritical CP [23][24][25][26][27][28]. In this modification, in addition to the ordinary CP, an inactive particle becomes active at a rate ω when it contacts two consecutive active particles.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium phase transition in an open quantum spin system with long-range interaction

Kahng

2019

Phys. Rev. E

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We investigate a nonequilibrium phase transition in a dissipative and coherent quantum spin system using the quantum Langevin equation and mean-field theory. Recently, the quantum contact process (QCP) was theoretically investigated using the Rydberg antiblockade effect, in particular, when the Rydberg atoms were excited in s-states so that their interactions were regarded as being between the nearest neighbors. However, when the atoms are excited to d-states, the dipole-dipole interactions become effective, and long-range interactions must be considered. Here, we consider a quantum spin model with a long-range QCP, where the branching and coagulation processes are allowed not only for the nearest-neighbor pairs, but also for long-distance pairs, coherently and incoherently. Using the semiclassical approach, we show that the mean-field phase diagram of our longrange model is similar to that of the nearest-neighbor QCP, where the continuous (discontinuous) transition is found in the weak (strong) quantum regime. However, at the tricritical point, we find a new universality class, which was neither that of the QCP at the tricritical point nor that of the classical directed percolation model with long-range interactions. Implementation of the long-range QCP using interacting cold gases is discussed. arXiv:1901.07682v2 [cond-mat.stat-mech]

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Section: Introductionmentioning

confidence: 99%

Nonequilibrium phase transition in an open quantum spin system with long-range interaction

Kahng

2019

Phys. Rev. E

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“…In fact, the STCP model was explored in Refs. [14][15][16] using slightly different rules, but the numerical values of their critical exponents differed from each other. The origin of this difference will be discussed later.…”

Section: A Stcp Model In Two Dimensionsmentioning

confidence: 99%

“…For instance, Lübeck introduced the so-called tricritical CP (TCP) model as follows. In addition to the ordinary CP, a pair of consecutive active particles can activate an inactive particle at a nearest-neighbor site with probability ω [14][15][16][17][18][19]. The TCP model exhibits an absorbing transition, which is either first-order or second-order depending on the parameters (κ, ω).…”

Section: Introductionmentioning

confidence: 99%

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Tricritical directed percolation with long-range interaction in one and two dimensions

Kahng

2020

Phys. Rev. E

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Recently, the quantum contact process, in which branching and coagulation processes occur both coherently and incoherently, was theoretically and experimentally investigated in driven open quantum spin systems. In the semi-classical approach, the quantum coherence effect was regarded as a process in which two consecutive atoms are involved in the excitation of a neighboring atom from the inactive (ground) state to the active state (excited s-state). In this case, both second-order and first-order transitions occur. Therefore, a tricritical point exists at which the transition belongs to the tricritical directed percolation (TDP) class. On the other hand, when an atom is excited to the d-state, long-range interaction is induced. Here, to account for this long-range interaction, we extend the TDP model to one with long-range interaction in the form of ∼ 1/r d+σ (denoted as LTDP), where r is the separation, d is the spatial dimension, and σ is a control parameter. In particular, we investigate the properties of the LTDP class below the upper critical dimension d c = min(3, 1.5σ). We numerically obtain a set of critical exponents in the LTDP class and determine the interval of σ for the LTDP class. Finally, we construct a diagram of universality classes in the space (d, σ). arXiv:1911.05964v3 [cond-mat.stat-mech] 31 Jan 2020

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“…In this paper, we examine a model where the order of the phase transition changes from continuous to first order for 1 < d f < 2. Following Lübeck and Grassberger's investigations of tricritical behaviour [8,9], we have previously investigated a modified version of this model in which both continuous and first-order phase transitions were numerically observed in 2D and above [10]. In the phase space, the two critical lines meet at a so-called tricritical point.…”

Section: Introductionmentioning

confidence: 99%

Change in order of phase transitions on fractal lattices

Windus

2009

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tWe re-examine a population model which exhibits a continuous absorbing phase transition belonging to directed percolation in 1D and a first-order transition in 2D and above. Studying the model on Sierpinski Carpets of varying fractal dimensions, we examine at what fractal dimension 1 ≤ d f ≤ 2, the change in order occurs. As well as commenting on the order of the transitions, we produce estimates for the critical points and, for continuous transitions, some critical exponents.

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Cluster geometry and survival probability in systems driven by reaction–diffusion dynamics

Cited by 5 publications

References 17 publications

Nonequilibrium phase transition in an open quantum spin system with long-range interaction

Nonequilibrium phase transition in an open quantum spin system with long-range interaction

Tricritical directed percolation with long-range interaction in one and two dimensions

Change in order of phase transitions on fractal lattices

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