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

Abstract

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 $\sim 1/r^{d+\sigma }$ (denoted as LTDP), where $r$ is the separation, $d$ is the spatial dimension, and $\sigma$ is a control parameter. In particular, we investigate the properties of the LTDP class below the upper critical dimension $d_c=$ min$(3,1.5\sigma )$. We numerically obtain a set of critical exponents in the LTDP class and determine the interval of $\sigma$ for the LTDP class. Finally, we construct a diagram of universality classes in the space ($d$, $\sigma$).

16 pages, 21 figures

References in corpus (31)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Antiblockade in Rydberg excitation of an ultracold lattice gas
• Evidence of antiblockade in an ultracold Rydberg gas
• Recent advances and open challenges in percolation
• Conformal Invariance in the Long-Range Ising Model
• Many-body theory of excitation dynamics in an ultracold Rydberg gas
• Levy-flight spreading of epidemic processes leading to percolating clusters
• The boundary between long-range and short-range critical behavior
• Long-range critical exponents near the short-range crossover
• Criticality in one dimension with inverse square-law potentials
• Absorbing state phase transition with competing quantum and classical fluctuations
• A model for anomalous directed percolation
• Experimental signatures of an absorbing-state phase transition in an open driven many-body quantum system
• Influence of long-range interactions on the critical behavior of the Ising model
• Non-equilibrium Phase Transitions with Long-Range Interactions
• Quantum contact process
• Tricritical directed percolation
• Upper and Lower Critical Decay Exponents of Ising Ferromagnets with Long-range Interaction
• Sampling methods for the quasistationary regime of epidemic processes on regular and complex networks
• Non-equilibrium effective field theory for absorbing state phase transitions in driven open quantum spin systems
• Tricritical directed percolation in 2+1 dimensions
• Two-dimensional SIR epidemics with long range infection
• Phenomenology of a First Order Dark State Phase Transition
• Numerical Simulation of Critical Dissipative Non-Equilibrium Quantum Systems with an Absorbing State
• Field theory of directed percolation with long-range spreading
• Long-range epidemic spreading with immunization
• Phase transitions in a lattice population model
• Nonequilibrium phase transition in an open quantum spin system with long-range interaction
• Contact processes with long-range interactions
• Cluster geometry and survival probability in systems driven by reaction-diffusion dynamics

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