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We study the problem of the crossover from one- to higher-dimensional metalsby considering an array of Luttinger liquids (one-dimensional chains) coupledby a weak interchain hopping {\tp.} We evaluate the exact asymptotic low-energybehavior of the self-energy in the anisotropic infinite-dimension limit. Thislimit extends the dinamical mean field concept to the case of a chain embeddedin a self-consistent medium. The system flows to a Fermi-liquid fixed point forenergies below the dimensional crossover temperature, and the anomalousexponent $\al$ renormalizes to zero, in the case of equal spin and chargevelocities. In particular, the single-particle spectral function shows sharpquasiparticle peaks with nonvanishing weight along the whole Fermi surface, incontrast to the lowest-order result. Our result is obtained by carring out aresummation of all diagrams of the expansion in \tp contributing to theanisotropic $D\to\infty$ limit. This is done by solving, in an almostcompletely analytic way, an asymptotically exact recursive equation for therenormalized vertices, within a skeleton expansion. Our outcome shows thatperturbation expansions in \tp restricted to lowest orders are unreliable belowthe crossover temperature. The extension to finite dimensions is discussed.This work extends our recent Letter [Phys. Rev. Lett. {\bf 83}, 128 (1999)],and includes all mathematical details.Comment: 29 pages, 13 eps figures. Contains all mathematical details of PRL  83, 128 (99) (cond-mat/9903431). Minor typos correcte

Crossover to Fermi-liquid behavior for weakly coupled Luttinger liquids in the anisotropic large-dimension limit