Universality of the weak pushed-to-pulled transition in systems with repulsive interactions

Abstract

We consider a $d$-dimensional gas in canonical equilibrium under pairwise screened Coulomb repulsion and external confinement, and subject to a volume constraint. We show that its excess free energy displays a generic third-order singularity separating the pushed and pulled phases, irrespective of range of the pairwise interaction, dimension and details of the confining potential. The explicit expression of the excess free energy is universal and interpolates between the Coulomb (long-range) and the delta (zero-range) interaction. The order parameter of this transition - the electrostatic pressure generated by the surface excess charge - is determined by invoking a fundamental energy conservation argument.

12 pages, 2 figures. Revised version

References in corpus (14)

• Large Deviations of Extreme Eigenvalues of Random Matrices
• Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices
• Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices
• Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
• Distributions of Conductance and Shot Noise and Associated Phase Transitions
• Exact extremal statistics in the classical $1d$ Coulomb gas
• A simple derivation of the Tracy-Widom distribution of the maximal eigenvalue of a Gaussian unitary random matrix
• Ground state of a confined Yukawa plasma including correlation effects
• Extremes of $2d$ Coulomb gas: universal intermediate deviation regime
• Universality of the third-order phase transition in the constrained Coulomb gas
• Complex saddles in the Gross-Witten-Wadia matrix model
• Joint statistics of quantum transport in chaotic cavities
• Fluctuations in the two-dimensional one-component plasma and associated fourth-order phase transition
• On the extreme value statistics of normal random matrices and 2D Coulomb gases: Universality and finite N corrections

Cited by in corpus (15)

• Extreme value statistics of correlated random variables: a pedagogical review
• Harmonically confined particles with long-range repulsive interactions
• Linear statistics and pushed Coulomb gas at the edge of beta random matrices: four paths to large deviations
• Edge fluctuations and third-order phase transition in harmonically confined long-range systems
• Third-order phase transition: random matrices and screened Coulomb gas with hard walls
• Particles confined in arbitrary potentials with a class of finite-ranged interactions
• Harmonically confined long-ranged interacting gas in the presence of a hard wall
• Spatio-temporal spread of perturbations in power-law models at low temperatures: Exact results for OTOC
• Finite temperature equilibrium density profiles of integrable systems in confining potentials
• Phase diagram of bipartite entanglement
• Full counting statistics of 1d short-range Riesz gases in confinement
• Complex (super)-matrix models with external sources and $q$-ensembles of Chern-Simons and ABJ(M) type
• Crossover in densities of confined particles with finite range of interaction
• Truncated linear statistics in the one dimensional one-component plasma
• Condensation of vanishing photon emission rates in random atomic clouds