Abstract
Various geometrical models first defined in the Euclidean plane or on a regular lattice have been briefly reviewed, including self-avoiding walks, random walk intersections, percolation and Ising clusters. These systems embody infinite sets of field operators defined in a natural way from the (fractal) geometry of these fluctuating critical systems. Their scaling behavior can be linked to that of associated conformal field theories. These systems can also all be redefined on a random lattice or surface, instead of on a regular 2D lattice. They are then coupled to ``quantum gravity``, and live on the ``world-sheet``. The fact that all their new exponents on a random surface can then be related to those in the usual 2D-plane, although now well known in string theory, is worth publicizing in this Physics in 2D conference. We illustrate it by some exact solutions in the case of polymers and branched polymers (animals) on a random fluid surface. (author).
Citation Formats
Duplantier, B.
Statistical mechanics on a 2D-random surface.
France: N. p.,
1991.
Web.
Duplantier, B.
Statistical mechanics on a 2D-random surface.
France.
Duplantier, B.
1991.
"Statistical mechanics on a 2D-random surface."
France.
@misc{etde_10136927,
title = {Statistical mechanics on a 2D-random surface}
author = {Duplantier, B}
abstractNote = {Various geometrical models first defined in the Euclidean plane or on a regular lattice have been briefly reviewed, including self-avoiding walks, random walk intersections, percolation and Ising clusters. These systems embody infinite sets of field operators defined in a natural way from the (fractal) geometry of these fluctuating critical systems. Their scaling behavior can be linked to that of associated conformal field theories. These systems can also all be redefined on a random lattice or surface, instead of on a regular 2D lattice. They are then coupled to ``quantum gravity``, and live on the ``world-sheet``. The fact that all their new exponents on a random surface can then be related to those in the usual 2D-plane, although now well known in string theory, is worth publicizing in this Physics in 2D conference. We illustrate it by some exact solutions in the case of polymers and branched polymers (animals) on a random fluid surface. (author).}
place = {France}
year = {1991}
month = {Dec}
}
title = {Statistical mechanics on a 2D-random surface}
author = {Duplantier, B}
abstractNote = {Various geometrical models first defined in the Euclidean plane or on a regular lattice have been briefly reviewed, including self-avoiding walks, random walk intersections, percolation and Ising clusters. These systems embody infinite sets of field operators defined in a natural way from the (fractal) geometry of these fluctuating critical systems. Their scaling behavior can be linked to that of associated conformal field theories. These systems can also all be redefined on a random lattice or surface, instead of on a regular 2D lattice. They are then coupled to ``quantum gravity``, and live on the ``world-sheet``. The fact that all their new exponents on a random surface can then be related to those in the usual 2D-plane, although now well known in string theory, is worth publicizing in this Physics in 2D conference. We illustrate it by some exact solutions in the case of polymers and branched polymers (animals) on a random fluid surface. (author).}
place = {France}
year = {1991}
month = {Dec}
}