Open Conference Systems, StatPhys 27 Main Conference

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On the mechanism behind the inverse melting in systems with competing interactions
Lucas Nicolao, Alejandro Mendoza-Coto, Rogelio Díaz-Méndez

##manager.scheduler.building##: Edificio San Jose Aula Magna
Date: 2019-07-12 11:30 AM – 11:45 AM
Last modified: 2019-06-08


The competition between a short-range attractive interaction and a nonlocal repulsive interaction promote the appearance of modulated phases. These can be observed in systems as diverse as mixtures of polymers, charged colloidal systems and magnetic thin films, where the modulation of the scalar order parameter develop spatial textures composed of stripes and bubbles (clusters) in two dimensions. In this work we present the microscopic mechanisms leading to the emergence of inverse transitions in such systems by considering a thorough mean-field analysis of a variety of minimal models with different competing interactions and by developing suitable coarse-grained numerical simulations. In an inverse melting transition, the more symmetric phase (homogeneous/liquid) is observed at lower temperatures, while the less symmetric phase (modulated/crystal) appears for higher temperatures, giving rise to a reentrant equilibrium phase diagram of external field/density against temperature. This counter-intuitive behavior can be attributed to the interplay between entropy and energy, generally by means of an entropy excess in the less symmetric phase. A first result shows that for reentrance to be appreciable, an interplay between entropy and energy can only be attained when the characteristic energy cost of the homogeneous and modulated phases are comparable to each other. In other words, the nonlocal repulsive interaction must be much weaker that the local attractive one. Our main result shows that the local excess entropy comes from the spatial regions where the order parameter is close to is saturation value. This mechanism also elucidates which systems and models can exhibit this kind of inverse transition, which are those that have a limited order parameter, such as particle systems with a hard-core or magnetic systems, where magnetization is naturally saturated. These mean field results are confirmed by simulations of an effective coarse-grained mesoscopic model. These are the first simulations of modulated phases presenting this kind of inverse transition, opening the way to numerical studies on length scales relevant to experiments.