BPCPPDYSOE21 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 32: Posters DY - Statistical Physics, Brownian Motion and Nonlinear Dynamics

DY 32.22: Poster

Dienstag, 23. März 2021, 16:30–19:00, DYp

Multiple Singularities of the Equilibrium Free Energy in a One-Dimensional Model of Soft Rods — •Juliane U. Klamser¹, Sushant Saryal², Tridib Sadhu³, and Deepak Dhar² — ¹Gulliver UMR CNRS 7083, ESPCI Paris, Université PSL, 75005 Paris, France — ²Indian Institute of Science Research and Education, Pashan, Pune 411008, India — ³Tata Institute of Fundamental Research, Mumbai 400005, India

The Landau-Peierls argument and the Perron-Frobenius theorem are frequently used to argue against the existence of equilibrium phase transitions in one dimension. We present a new mechanism for the emergence of singularities in the thermodynamic free energy even in one dimension. This mechanism is observed in an instructive model of thin, rigid, linear rods of equal length 2ℓ whose centers lie on a one-dimensional lattice, of lattice spacing a. The interaction between rods is a soft-core interaction, having a finite energy U per overlap of rods. By solving the model analytically, we show that the equilibrium free energy per rod F(ℓa,β), at inverse temperature β, has an infinite number of singularities, as a function of ℓa. A two-dimensional extension of this model shows an interesting combination of two kinds of phase transitions, which we understand by an exact solution on the Bethe lattice.