Phase Transition in Growing Causal Networks and Possible Dynamical Preference of Spatial Dimension
Year: 2026
Type: article
Abstract: We study phase transitions in growing causal networks in which spatial connectivityemerges from an underlying temporal order. Introducing a “zero-connectivity” regime, wedemonstrate the existence of a percolation transition with analytically estimated criticalpointαc =1− 12k .Numerical simulations confirm the transition and yield critical exponents consistent withthree-dimensional percolation behavior.Wefurther consider a scalar ϕ4 field theory defined on the critical network. Renormalization group arguments indicate that within the interval 2 < ds < 4, where non-trivial infraredfixed points may exist, the value ds ≈ 3 occupies a dynamically favorable regime associatedwith non-mean-field behavior. While this does not constitute a proof of dimensional selection, it suggests a possible mechanism by which three-dimensional space could emerge as acritical phenomenon from purely causal constraints, with time remaining fundamental in allphases.
Author: Gimranov, Alik
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7131293260
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