β Scribed by Attilio Stella
No coin nor oath required. For personal study only.
Recent results concerning the statistics of self-avoiding random surfaces (SAS) and vesicles made of elementary lattice plaquettes in d = 3 are reviewed. In all cases progress follows from introduction of spin or gauge Ising vacancies into a suitable gauge model with n-component classical vectors as degrees of freedom. SAS statistics is generated in the n ~ 0 limit. Topics include in particular the possibility of defining SAS models with the geometry of Ising spin cluster hulls, crossover from SAS to deflated vesicles, and the role of topology in determining the universality class of SAS problems. Critical properties of SAS models in the presence of an adsorbing boundary plane are also discussed.
π SIMILAR VOLUMES
The complications encountered in direct renormalization approaches for the self-avoiding walk problem are discussed. Using a decimation transformation on the square lattice, sequences of approximants to the critical exponent Y and to the inverse connective constant K,(l/K, = ~1 are obtained.