Collective dynamics in lattice models far from equilibrium

In this thesis, we explore the large-scale collective dynamics of lattice models that are far from equilibrium due to disorder, external driving, metastability and activity. First, we investigate the non-equilibrium behaviour of the three-dimensional random field Ising model at finite temperature, as an external field is increased through its coercive field. We show by numerical simulations that the phenomenology of avalanches—which are sharply defined only at zero temperature—also persists over a significant range of finite temperatures. We analyse the main differences between the thermal and zero-temperature systems, including an excess of small avalanches in the thermal case, whose behaviour is consistent with activated dynamical scaling. We also investigate the extent to which individual avalanches at finite temperature can be traced back to parent avalanches in the athermal system. Then, we investigate the nucleation dynamics of the same model under a fixed external field. We use umbrella sampling to compute the free-energy cost of a critical nucleus and use forward flux sampling for the direct estimation of nucleation rates. For moderate to strong disorder, our results indicate that the size of the nucleating cluster is not a good reaction coordinate, contrary to the pure Ising model. We rectify this problem by introducing a coordinate that also accounts for the location of the nucleus. Using the free energy barrier to predict the nucleation rate, we find reasonable agreement, although deviations become stronger as disorder increases. We attribute this effect to cluster shape fluctuations. We also discuss finite-size effects on the nucleation rate. Finally, we analyse motility-induced phase coexistence in a lattice model of self-propelled particles. We compare two-dimensional systems where the dense phase has both slab and droplet geometries. In the slab geometry, we measure the spectrum of the height profile of the liquid-vapour interface, finding it consistent with capillary wave theory at long wavelengths. The density fluctuations inside the liquid phase show features of bubbly phase separation, but the capillary wave fluctuations are agnostic to these bubbles due to a separation of timescales. The density of the dilute phase is shifted by a Laplace pressure effect that arises from the curvature of the droplet, but the dense phase has stronger fluctuations than predicted by equilibrium-like hydrodynamic theories. We observe a strong numerical correspondence between the surface tensions that govern the Laplace pressure effect and capillary wave statistics.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2024

Author dc:creator

• Yao, Liheng

Advisor dc:contributor.advisor

• Jack, Robert

• Monte Carlo methods
• statistical physics
• phase transitions
• disordered systems
• active matter

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/93f495c2-1221-4342-91ea-789e604c0296/download
• https://creativecommons.org/licenses/by/4.0/

Language dc:language

eng

Author Identifier

0009-0006-5309-8437

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/377403