TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.5.219
TI  - Dynamical mean field theory for models of confluent tissues and beyond
PY  - 2023/11/30
UR  - https://www.scipost.org/SciPostPhys.15.5.219
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 5
SP  - 219
A1  - Kamali, Persia Jana
AU  - Urbani, Pierfrancesco
AB  - We consider a recently proposed model to understand the rigidity transition in confluent tissues and we derive the dynamical mean field theory (DMFT) equations that describes several types of dynamics of the model in the thermodynamic limit: gradient descent, thermal Langevin noise and active drive. In particular we focus on gradient descent dynamics and we integrate numerically the corresponding DMFT equations. In this case we show that gradient descent is blind to the zero temperature replica symmetry breaking (RSB) transition point. This means that, even if the Gibbs measure in the zero temperature limit displays RSB, this algorithm is able to find its way to a zero energy configuration. We include a discussion on possible extensions of the DMFT derivation to study problems rooted in high-dimensional regression and optimization via the square loss function.
ER  -

@Article{10.21468/SciPostPhys.15.5.219,
	title={{Dynamical mean field theory for models of confluent tissues and beyond}},
	author={Persia Jana Kamali and Pierfrancesco Urbani},
	journal={SciPost Phys.},
	volume={15},
	pages={219},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.5.219},
	url={https://scipost.org/10.21468/SciPostPhys.15.5.219},
}