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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.14224 |
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| _version_ | 1866912129525743616 |
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| author | Joshi, Divya D. Gade, Prashant M. |
| author_facet | Joshi, Divya D. Gade, Prashant M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14224 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cellular Automata model for period-$n$ synchronization: A new universality class Joshi, Divya D. Gade, Prashant M. Statistical Mechanics 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. |
| title | Cellular Automata model for period-$n$ synchronization: A new universality class |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2406.14224 |