Slow activity decay in excitable models with discontinuous phase transitions
Abstract
As a simple model of interacting systems of excitable degrees of freedom, we consider a threshold contact process on various lattices and networks, in which a successful activation event requires the presence of more than one active neighbors. We show by combining numerical simulations and a phenomenological theory that, in the two-phase coexistence region and for a sufficiently low initial activity, a slower-than-exponential temporal decay of the global density emerges, caused by the spontaneous formation of slowly vanishing and non-communicating clusters of activity. This slow-decay phenomenon is found to appear generally for regular lattices and also for finite-dimensional random lattices such as the Voronoi-Delaunay network. However, the slow-decay is impeded by small-world property, as demonstrated by simulations on random-regular networks. In the case of a power-law decay of the order parameter, which is valid among others on two-dimensional regular lattices, our phenomenological theory points out that the decaying state is stable against unbounded nucleation only if the decay exponent exceeds 1/2. Besides the well-known Griffiths effects of quenched random systems, this slow-decay phenomenon rooted in the threshold condition provides an alternative mechanism of off-critical but scale-free dynamics, occurring also in the absence of disorder.
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BibTeX
@misc{lorenzoni2026slow,
title = {{Slow activity decay in excitable models with discontinuous phase transitions}},
author = {Paulo H. Lorenzoni and Géza Ódor and Silvio C. Ferreira and Róbert Juhász},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12862},
eprint = {2609.12862},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12862},
}
RIS
TY - UNPB
TI - Slow activity decay in excitable models with discontinuous phase transitions
AU - Paulo H. Lorenzoni
AU - Géza Ódor
AU - Silvio C. Ferreira
AU - Róbert Juhász
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12862
UR - https://arxiv.org/abs/2609.12862
AB - As a simple model of interacting systems of excitable degrees of freedom, we consider a threshold contact process on various lattices and networks, in which a successful activation event requires the presence of more than one active neighbors. We show by combining numerical simulations and a phenomenological theory that, in the two-phase coexistence region and for a sufficiently low initial activity, a slower-than-exponential temporal decay of the global density emerges, caused by the spontaneous formation of slowly vanishing and non-communicating clusters of activity. This slow-decay phenomenon is found to appear generally for regular lattices and also for finite-dimensional random lattices such as the Voronoi-Delaunay network. However, the slow-decay is impeded by small-world property, as demonstrated by simulations on random-regular networks. In the case of a power-law decay of the order parameter, which is valid among others on two-dimensional regular lattices, our phenomenological theory points out that the decaying state is stable against unbounded nucleation only if the decay exponent exceeds 1/2. Besides the well-known Griffiths effects of quenched random systems, this slow-decay phenomenon rooted in the threshold condition provides an alternative mechanism of off-critical but scale-free dynamics, occurring also in the absence of disorder.
ER -