Condensed Matter Theory

Abstract:

We analyze the thermodynamic properties of the random-bond Ising model (RBIM) on closed hyperbolic surfaces using Monte Carlo and high-temperature series expansion techniques. We also analyze the dual-RBIM, that is, the model that in the absence of disorder is related to the RBIM via the Kramers-Wannier duality. Even on self-dual lattices this model is different from the RBIM, unlike in the Euclidean case. We explain this anomaly by a careful rederivation of the Kramers-Wannier duality. For the (dual-)RBIM, we compute the paramagnet-to-ferromagnet phase transition as a function of both temperature T and the fraction of antiferromagnetic bonds p. We find that as temperature is decreased in the RBIM, the paramagnet gives way to either a ferromagnet or a spin-glass phase via a second-order transition compatible with mean-field behavior. In contrast, the dual-RBIM undergoes a strongly first-order transition from the paramagnet to the ferromagnet both in the absence of disorder and along the Nishimori line. We study both transitions for a variety of hyperbolic tessellations and comment on the role of coordination number and curvature. The extent of the ferromagnetic phase in the dual-RBIM corresponds to the correctable phase of hyperbolic surface codes under independent bit- and phase-flip noise.

Abstract:

We use a computational phase-field model together with analytical analysis to study how intercellular active forces can mediate individual cell morphology and collective motion in a confluent cell monolayer. We explore the regime where intercellular forces dominate the tissue dynamics, and polar forces are negligible. Contractile intercellular interactions lead to cell elongation, nematic ordering, and active turbulence characterized by motile topological defects. Extensile interactions result in frustration, and perpendicular cell orientations become more prevalent. Furthermore, we show that contractile behavior can change to extensile behavior if anisotropic fluctuations in cell shape are considered.