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Crumpling transition and flat phase of polymerized phantom membranes

Crumpling transition and flat phase of polymerized phantom membranes

Polymerized phantom membranes are revisited using a nonperturbative renormalization-group approach. This allows one to investigate both the crumpling transition and the low-temperature flat phase in any internal dimension D and embedding dimension d and to determine the lower critical dimension. The crumpling phase transition for physical membranes is found to …