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Freezing phase transition in a fractal potential
CESAR OCTAVIO MALDONADO AHUMADA
RAUL SALGADO GARCIA
Acceso Abierto
Atribución-NoComercial-SinDerivadas
https://doi.org/10.1088/1742-5468/ab02f5
Exact results
"In this work we propose a simple example of a one-dimensional thermodynamic system where non-interacting particles are allowed to move over the [0, 1] interval, which are influenced by a potential with a fractal structure. We prove that the system exhibits a phase transition at a finite temperature, which is characterized by the fact that the Gibbs-Boltzmann probability measure passes from being absolutely continuous with respect to Lebesgue (at high temperatures) to being singular continuous (at low temperatures). We prove that below the critical temperature (when the Gibbs-Boltzmann probability measure is singular continuous) the probability measure is supported on the middle-third Cantor set and that further lowering the temperature, the probability measure does not change anymore. This means that, in some sense, the system reaches the ground-state before the zero temperature, indicating that the system 'freezes' at a positive temperature."
IOP Publishing
2019
Artículo
Cesar Maldonado and R Salgado-García J. Stat. Mech. (2019) 033203
MATEMÁTICAS
Versión revisada
submittedVersion - Versión revisada
Aparece en las colecciones: Publicaciones Científicas Control y Sistemas Dinámicos

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