Universality of the third-order phase transition in the constrained Coulomb gas

Abstract

The free energy at zero temperature of Coulomb gas systems in generic dimension is considered as a function of a volume constraint. The transition between the 'pulled' and the 'pushed' phases is characterised as a third-order phase transition, in all dimensions and for a rather large class of isotropic potentials. This suggests that the critical behaviour of the free energy at the 'pulled-to-pushed' transition may be universal, i.e., to some extent independent of the dimension and the details of the pairwise interaction.

18 pages, 2 figures. v2: References added

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• Harmonically confined particles with long-range repulsive interactions
• Universality of the weak pushed-to-pulled transition in systems with repulsive interactions
• Edge fluctuations and third-order phase transition in harmonically confined long-range systems
• Current fluctuations in stochastically resetting particle systems
• Gap probability and full counting statistics in the one dimensional one-component plasma
• Particles confined in arbitrary potentials with a class of finite-ranged interactions
• Third-order phase transition: random matrices and screened Coulomb gas with hard walls
• Exact equivalences and phase discrepancies between random matrix ensembles
• Critical exponents for higher order phase transitions: Landau theory and RG flow
• Universal behavior of the full particle statistics of one-dimensional Coulomb gases with an arbitrary external potential
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• Macroscopic and edge behavior of a planar jellium
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• Phase diagram of bipartite entanglement
• Crossover in densities of confined particles with finite range of interaction
• Complex (super)-matrix models with external sources and $q$-ensembles of Chern-Simons and ABJ(M) type
• Equilibrium measures for higher dimensional rotationally symmetric Riesz gases
• Edge behavior of two-dimensional Coulomb gases near a hard wall
• PhD thesis "Extreme value statistics of strongly correlated systems: fermions, random matrices and random walks"
• Two dimensional Coulomb gas in a non-conservative trap
• Phase transition in the diffusion and bootstrap percolation models on regular random and Erdős-Rényi networks