Novel transition to fully absorbing state without long-range spatial order in directed percolation class

We study coupled Gauss maps in one dimension with nearest-neighbor interactions. We observe transitions from spatiotemporal chaos to period-3 states in a coarse-grained sense and synchronized period-3 states. Synchronized fixed points are frequently observed in one dimension. However, synchronized periodic states are rare. The obvious reason is that it is very easy to create defects in one dimension. We characterize all transitions using the following order parameter. Let x∗ be the fixed point of the map. The values above (below) x∗ are classified as +1 (−1) spins. We expect all sites to return to the same band after three time steps for a coarse-grained periodic or three-period state. We define the flip rate F(t) as the fraction of sites i such that si(3t−3)≠si(t). It is zero in the coarse-grained periodic state. This state may or may not be synchronized. We observe three different transitions. (a) If different sites reach different bands, the transition is in the directed-percolation universality class. (b) If all sites reach the same band, we find an Ising-type transition. (c) A synchronized period-3 state where a new exponent is observed. We also study the finite-size scaling at critical points. The exponents obtained indicate that the synchronized period-3 transition is in a new universality class.

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Cellular automata model for period-n synchronization: a new universality class

Joshi,

Gade

2024

J. Phys. A: Math. Theor.

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There are few known universality classes of absorbing phase transitions in one dimension and most models fall in the well-known directed percolation (DP) class. Synchronization is a transition to an absorbing state and this transition is often DP class. With local coupling, the transition is often to a fixed point state. Transitions to a periodic synchronized state are possible. We model those using a cellular automata model with states 1 to $n$. The rules are a) Each site in state $i$ changes to state $i+1$ for $i<n$ and 1 if $i=n$. b) After this update, it takes the value of either neighbour unless it is in state 1. With these rules, we observe a transition to synchronization with critical exponents different from those of DP for $n>2$. For $n=2$, a different exponent is observed.

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Novel transition to fully absorbing state without long-range spatial order in directed percolation class

Cited by 7 publications

References 31 publications

Approach to zigzag and checkerboard patterns in spatially extended systems

Approach to zigzag and checkerboard patterns in spatially extended systems

Transition to period-3 synchronized state in coupled gauss maps

Cellular automata model for period-n synchronization: a new universality class

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