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Low-dimensional phase transitions in and outside equilibrium

Abstract : Although nature is three-dimensional, lower dimensional systems are often effectively realized offering fascinating new physics. The subject of this thesis is phase transitions in low dimensions, with its primary focus on non-equilibrium phases in two-dimensional active matter. Unlike passive systems, active particles are driven by energy injected at the microscopic scale from internal degrees of freedom resulting in an irreversible dynamics, often giving rise to macroscopic phases in striking contrast to equilibrium. A goal is to give a quantitative characterization of such non-equilibrium phases and to capture these in simplest realizations of active matter. The thesis explores two-dimensional self-propelled particles with isotropic pair-wise interactions. The dynamics (persistent kinetic Monte Carlo) is a variant of passive disks and different from well-known models of active matter. A full quantitative phase diagram is presented including motility induced phase separation (MIPS) as seen in other active systems. Additionally, the famous two-step melting scenario with the hexatic phase extends far from equilibrium. In this non-equilibrium scenario, the activity can melt a 2D solid and the melting lines remain separated from MIPS. The second part explores a frequently debated issue of the existence of phase transitions in classical one-dimensional models with short-range interactions at non-zero temperature. A widely shared misconception is that such transitions are not possible. A clear counterexample to this belief is given where non-analyticity in the free energy emerges from a new mechanism with a geometrical origin, which is then established on a rigorous ground.
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Submitted on : Thursday, June 11, 2020 - 6:55:18 PM
Last modification on : Thursday, October 29, 2020 - 3:01:55 PM


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  • HAL Id : tel-02865332, version 2


Juliane Uta Klamser. Low-dimensional phase transitions in and outside equilibrium. Data Analysis, Statistics and Probability []. Sorbonne Université, 2018. English. ⟨NNT : 2018SORUS333⟩. ⟨tel-02865332v2⟩