Numéro |
J. Phys. I France
Volume 2, Numéro 5, May 1992
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|
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Page(s) | 599 - 613 | |
DOI | https://doi.org/10.1051/jp1:1992169 |
J. Phys. I France 2 (1992) 599-613
Crumpled glass phase of randomly polymerized membranes in the large d limit
Leo Radzihovsky and Pierre Le DoussalDapartment of Physics, Harvard University, Cambrige, Massachusetts 02138, U.S.A.
(Received 6 December 1991, accepted 28 January 1992)
Abstract
Tethered phantom membranes with quenched disorder in the internal preferred metric are studied in the limit of large embedding
space dimension
. We find that the instability of the flat phase previously demonstrated via
-expansion is towards a spin-glass-like phase which we call the crumpled glass phase. We propose a spin-glass order parameter
that characterizes this phase and derive the free energy which describes the crumpled, flat and crumpled glass phases is described
by local tangents which vanish on average, but display a nonzero Edwards-Anderson spin-glass order parameter. From the saddle
point equations at large
d we obtain the equation of state, phase diagram and the exponents characterizing these phases. We estimate the effects of
the higher order corrections in the
1/d expansion by utilizing previous results for pure membranes. We use Flory arguments to calculate the wandering exponents and
discuss the relevance of self-avoidance in the crumpled glass phase.
© Les Editions de Physique 1992