2023/09/16 by Rodrigue Lelotte, Lelotte, Rodrigue · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2309.08951
openalex publication_date 2023/09/16 · openalex created_date 2023/09/20 · openalex updated_date 2026/07/30
We provide numerical evidence for the existence of phase transitions with respect to the temperature in the one-dimensional Riesz gases with non-singular pair interaction, that is particles on the line interacting via the potential -|r|-s, where s ∈ (-1, 0). Our numerics hint for the existence of two distinct phase transitions whose critical temperatures depend on s, namely a first transition which separates between a fluid and a quasisolid phase reminiscent of the Berezinski-Kosterlitz-Thouless (BKT) transition, and a second transition below which freezing occurs and the system is in a solid phase. We determine the phase diagram with respect to s and the temperature T, which we find to be consistent with the known (or expected) results on the 1D Coulomb gas (s = -1), known to be a solid at all temperature, and the Dyson log--gas (s = 0) which exhibits a BKT transition at T = 1/2 and which is believed to be a fluid at all positive temperature.