Thermodynamical behavior of polymerized membranes

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Abstract
We analyze by field theoretical methods the thermodynamical behavior of polymerized membranes, fluctuating without excluded volume interactions and in presence of either free or constrained boundary conditions. We highlight the nature of the crumpling transition, by showing how the tension arising in the presence of constrained boundary conditions may be considered as the field conjugate to the corresponding order parameter. The low temperature flat phase of membranes with free boundary conditions is viewed as a critical phase corresponding to the buckling transition. We present the explicit solution, in the large d limit, of the elastic model of fluctuating elastic membranes and we complete the renormalization of the fluctuations in the flat phase