Pierpaolo Vivo — King's College London #
Universality of third-order phase transition for constrained Coulomb gases #
The free energy at zero temperature of Coulomb gas systems in generic dimension is considered as a function of a volume constraint, i.e. by varying the total volume available to the system. The transition between the 'pulled' and the 'pushed' phases of the gas is characterised as a third-order phase transition, in any dimension 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. In particular, the logarithmic pairwise interaction, typical of random matrix problems where a similar third-order transition was previously detected, does not play any special role.