1,900 research outputs found
Gibbs-non-Gibbs properties for n-vector lattice and mean-field models
We review some recent developments in the study of Gibbs and non-Gibbs
properties of transformed n-vector lattice and mean-field models under various
transformations. Also, some new results for the loss and recovery of the Gibbs
property of planar rotor models during stochastic time evolution are presented.Comment: 31 pages, 6 figure
Patch-repetition correlation length in glassy systems
We obtain the patch-repetition entropy Sigma within the Random First Order
Transition theory (RFOT) and for the square plaquette system, a model related
to the dynamical facilitation theory of glassy dynamics. We find that in both
cases the entropy of patches of linear size l, Sigma(l), scales as s_c l^d+A
l^{d-1} down to length-scales of the order of one, where A is a positive
constant, s_c is the configurational entropy density and d the spatial
dimension. In consequence, the only meaningful length that can be defined from
patch-repetition is the cross-over length xi=A/s_c. We relate xi to the typical
length-scales already discussed in the literature and show that it is always of
the order of the largest static length. Our results provide new insights, which
are particularly relevant for RFOT theory, on the possible real space structure
of super-cooled liquids. They suggest that this structure differs from a mosaic
of different patches having roughly the same size.Comment: 6 page
Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity
In a recent work, a dual formulation of group field theories as
non-commutative quantum field theories has been proposed, providing an exact
duality between spin foam models and non-commutative simplicial path integrals
for constrained BF theories. In light of this new framework, we define a model
for 4d gravity which includes the Immirzi parameter gamma. It reproduces the
Barrett-Crane amplitudes when gamma goes to infinity, but differs from existing
models otherwise; in particular it does not require any rationality condition
for gamma. We formulate the amplitudes both as BF simplicial path integrals
with explicit non-commutative B variables, and in spin foam form in terms of
Wigner 15j-symbols. Finally, we briefly discuss the correlation between
neighboring simplices, often argued to be a problematic feature, for example,
in the Barrett-Crane model.Comment: 26 pages, 1 figur
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