Nonequilibrium Steady States and Phase Transitions

Guha Ray, Chandraniva (2023) Nonequilibrium Steady States and Phase Transitions. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Chandraniva Guha Ray (18MS143)) Thesis_18MS143.pdf - Submitted Version Restricted to Repository staff only Download (917kB)

Abstract

Non-equilibrium systems are ubiquitous in nature, but solutions to higher dimensional latticebased systems has not been studied analytically in great detail. On the other hand, the matrix product ansatz (MPA) formalism has been considerably successful in describing the exact solutions of one dimensional out-of-equilibrium systems. In the first half of the report, we extend the formalism to 2-dimensional lattice-based models, which in general may be anisotropic. We demonstrate how it works for 2D Ising spins and follow that by analyzing a non-equilibrium lattice gas dynamics which destroys consecutive 0’s. The critical exponents for the system are analyzed and compared with numerical simulations. Lastly, the dynamics is extended to an anistropic one, analyzed for small systems, and compared with simulations. It is concluded that our methodology is the natural extension of the MPA formalism to 2-dimensions, and serves as a novel approach to tackle 2-dimensional lattice-based systems. In the second half of the report, we shall discuss phase separation transitions in motile active matter systems. Particularly, we ask whether motility helps or hinders the ordering if a phase separated state was already present in the corresponding passive particle system. We show that indeed motility is detrimental to phase separation. Thus, without interaction within the dynamics, phase separation transitions generally do not occur.

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