The influence of long-range self-avoiding forces on the statistical mechanics of a D-dimensional tethered membrane is studied in the limit of large embedding space dimension d to infinity . The author finds three distinct isotropic (crumpled) phases and several flat phases, and thermally driven crumpling transitions for D>2. The effect of attraction and of short-range repulsion for D>2 is also discussed.
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Pierre Le Doussal (1992) studied this question.
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