Finite-volume statistical mechanics of two-component Coulomb-like systems and the principle of macroscopic equivalence

Classical stable charge-symmetric two-component systems are discussed in a fixed domain Λ⊂ℝ^d. The limit N→∞ of the finite-N canonical Gibbs ensemble is compared with the results obtained from a discussion of the Gibbs measures on the space of infinite configurations (the states). A first-order phase transition in the Gibbs states is proved for a large class of interactions, including regularized Coulomb interactions for d≧3. In the latter case the transition is isomorphic to an implosion/explosion transition in regularized gravitational systems. Spherical symmetry is not assumed. A transition occurs for certain largedomain/low-temperature pairs (Λ, β^∓1), but ceases to exist in the infinite-volume ensemble. The phase transition supports the conjecture that the standard thermodynamic-limit sequence can be nonuniform even for standard H-stable Hamiltonians. The results about the limit of the finite-N ensemble are less complete due to lack of sufficient control of the correlations. However, some notable differences between both descriptions are shown, which are cuased by noncommuting limits. Possible physical consequences and open questions are pointed out.