641 research outputs found
End to end distance on contour loops of random gaussian surfaces
A self consistent field theory that describes a part of a contour loop of a
random Gaussian surface as a trajectory interacting with itself is constructed.
The exponent \nu characterizing the end to end distance is obtained by a Flory
argument. The result is compared with different previuos derivations and is
found to agree with that of Kondev and Henley over most of the range of the
roughening exponent of the random surface.Comment: 7 page
Loop models on random maps via nested loops: case of domain symmetry breaking and application to the Potts model
We use the nested loop approach to investigate loop models on random planar
maps where the domains delimited by the loops are given two alternating colors,
which can be assigned different local weights, hence allowing for an explicit
Z_2 domain symmetry breaking. Each loop receives a non local weight n, as well
as a local bending energy which controls loop turns. By a standard cluster
construction that we review, the Q = n^2 Potts model on general random maps is
mapped to a particular instance of this problem with domain-non-symmetric
weights. We derive in full generality a set of coupled functional relations for
a pair of generating series which encode the enumeration of loop configurations
on maps with a boundary of a given color, and solve it by extending well-known
complex analytic techniques. In the case where loops are fully-packed, we
analyze in details the phase diagram of the model and derive exact equations
for the position of its non-generic critical points. In particular, we
underline that the critical Potts model on general random maps is not self-dual
whenever Q \neq 1. In a model with domain-symmetric weights, we also show the
possibility of a spontaneous domain symmetry breaking driven by the bending
energy.Comment: 44 pages, 13 figure
An Intersecting Loop Model as a Solvable Super Spin Chain
In this paper we investigate an integrable loop model and its connection with
a supersymmetric spin chain. The Bethe Ansatz solution allows us to study some
properties of the ground state. When the loop fugacity lies in the physical
regime, we conjecture that the central charge is for integer .
Low-lying excitations are examined, supporting a superdiffusive behavior for
. We argue that these systems are interesting examples of integrable
lattice models realizing conformal field theories.Comment: latex file, 7 page
Logarithmic corrections in the aging of the fully-frustrated Ising model
We study the dynamics of the critical two-dimensional fully-frustrated Ising
model by means of Monte Carlo simulations. The dynamical exponent is estimated
at equilibrium and is shown to be compatible with the value . In a
second step, the system is prepared in the paramagnetic phase and then quenched
at its critical temperature . Numerical evidences for the existence of
logarithmic corrections in the aging regime are presented. These corrections
may be related to the topological defects observed in other fully-frustrated
models. The autocorrelation exponent is estimated to be as for the
Ising chain quenched at .Comment: 12 pages, 9 figure
Shear-induced anisotropic decay of correlations in hard-sphere colloidal glasses
Spatial correlations of microscopic fluctuations are investigated via
real-space experiments and computer simulations of colloidal glasses under
steady shear. It is shown that while the distribution of one-particle
fluctuations is always isotropic regardless of the relative importance of shear
as compared to thermal fluctuations, their spatial correlations show a marked
sensitivity to the competition between shear-induced and thermally activated
relaxation. Correlations are isotropic in the thermally dominated regime, but
develop strong anisotropy as shear dominates the dynamics of microscopic
fluctuations. We discuss the relevance of this observation for a better
understanding of flow heterogeneity in sheared amorphous solids.Comment: 6 pages, 4 figure
On FPL configurations with four sets of nested arches
The problem of counting the number of Fully Packed Loop (FPL) configurations
with four sets of a,b,c,d nested arches is addressed. It is shown that it may
be expressed as the problem of enumeration of tilings of a domain of the
triangular lattice with a conic singularity. After reexpression in terms of
non-intersecting lines, the Lindstr\"om-Gessel-Viennot theorem leads to a
formula as a sum of determinants. This is made quite explicit when
min(a,b,c,d)=1 or 2. We also find a compact determinant formula which generates
the numbers of configurations with b=d.Comment: 22 pages, TeX, 16 figures; a new formula for a generating function
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Boundary and Bulk Phase Transitions in the Two Dimensional Q > 4 State Potts Model
The surface and bulk properties of the two-dimensional Q > 4 state Potts
model in the vicinity of the first order bulk transition point have been
studied by exact calculations and by density matrix renormalization group
techniques. For the surface transition the complete analytical solution of the
problem is presented in the limit, including the critical and
tricritical exponents, magnetization profiles and scaling functions. According
to the accurate numerical results the universality class of the surface
transition is independent of the value of Q > 4. For the bulk transition we
have numerically calculated the latent heat and the magnetization discontinuity
and we have shown that the correlation lengths in the ordered and in the
disordered phases are identical at the transition point.Comment: 11 pages, RevTeX, 6 PostScript figures included. Manuscript
substantially extended, details on the analytical and numerical calculations
added. To appear in Phys. Rev.
Nonequilibrium dynamics of fully frustrated Ising models at T=0
We consider two fully frustrated Ising models: the antiferromagnetic
triangular model in a field of strength, , as well as the Villain
model on the square lattice. After a quench from a disordered initial state to
T=0 we study the nonequilibrium dynamics of both models by Monte Carlo
simulations. In a finite system of linear size, , we define and measure
sample dependent "first passage time", , which is the number of Monte
Carlo steps until the energy is relaxed to the ground-state value. The
distribution of , in particular its mean value, , is shown to
obey the scaling relation, , for both models.
Scaling of the autocorrelation function of the antiferromagnetic triangular
model is shown to involve logarithmic corrections, both at H=0 and at the
field-induced Kosterlitz-Thouless transition, however the autocorrelation
exponent is found to be dependent.Comment: 7 pages, 8 figure
A Transfer Matrix for the Backbone Exponent of Two-Dimensional Percolation
Rephrasing the backbone of two-dimensional percolation as a monochromatic
path crossing problem, we investigate the latter by a transfer matrix approach.
Conformal invariance links the backbone dimension D_b to the highest eigenvalue
of the transfer matrix T, and we obtain the result D_b=1.6431 \pm 0.0006. For a
strip of width L, T is roughly of size 2^{3^L}, but we manage to reduce it to
\sim L!. We find that the value of D_b is stable with respect to inclusion of
additional ``blobs'' tangent to the backbone in a finite number of points.Comment: 19 page
Harmonic Measure and Winding of Conformally Invariant Curves
The exact joint multifractal distribution for the scaling and winding of the
electrostatic potential lines near any conformally invariant scaling curve is
derived in two dimensions. Its spectrum f(alpha,lambda) gives the Hausdorff
dimension of the points where the potential scales with distance as while the curve logarithmically spirals with a rotation angle
phi=lambda ln r. It obeys the scaling law f(\alpha,\lambda)=(1+\lambda^2)
f(\bar \alpha)-b\lambda^2 with \bar \alpha=\alpha/(1+\lambda^2) and
b=(25-c)/{12}$, and where f(\alpha)\equiv f(\alpha,0) is the pure harmonic
measure spectrum, and c the conformal central charge. The results apply to O(N)
and Potts models, as well as to {\rm SLE}_{\kappa}.Comment: 3 figure
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