840 research outputs found
Liouville Field Theory of Fluctuating Loops
Effective field theories of two-dimensional lattice models of fluctuating
loops are constructed by mapping them onto random surfaces whose large scale
fluctuations are described by a Liouville field theory. This provides a
geometrical view of conformal invariance in two-dimensional critical phenomena
and a method for calculating critical properties of loop models exactly. As an
application of the method, the conformal charge and critical exponents for two
mutually excluding Hamiltonian walks on the square lattice are calculated.Comment: 4 RevTex pages, 1 eps figur
Conformational Entropy of Compact Polymers
Exact results for the scaling properties of compact polymers on the square
lattice are obtained from an effective field theory. The entropic exponent
\gamma=117/112 is calculated, and a line of fixed points associated with
interacting chains is identified; along this line \gamma varies continuously.
Theoretical results are checked against detailed numerical transfer matrix
calculations, which also yield a precise estimate for the connective constant
\kappa=1.47280(1).Comment: 4 pages, 1 figur
Statistical Topography of Glassy Interfaces
Statistical topography of two-dimensional interfaces in the presence of
quenched disorder is studied utilizing combinatorial optimization algorithms.
Finite-size scaling is used to measure geometrical exponents associated with
contour loops and fully packed loops. We find that contour-loop exponents
depend on the type of disorder (periodic ``vs'' non-periodic) and they satisfy
scaling relations characteristic of self-affine rough surfaces. Fully packed
loops on the other hand are unaffected by disorder with geometrical exponents
that take on their pure values.Comment: 4 pages, REVTEX, 4 figures included. Further information can be
obtained from [email protected]
The packing of two species of polygons on the square lattice
We decorate the square lattice with two species of polygons under the
constraint that every lattice edge is covered by only one polygon and every
vertex is visited by both types of polygons. We end up with a 24 vertex model
which is known in the literature as the fully packed double loop model. In the
particular case in which the fugacities of the polygons are the same, the model
admits an exact solution. The solution is obtained using coordinate Bethe
ansatz and provides a closed expression for the free energy. In particular we
find the free energy of the four colorings model and the double Hamiltonian
walk and recover the known entropy of the Ice model. When both fugacities are
set equal to two the model undergoes an infinite order phase transition.Comment: 21 pages, 4 figure
Monte-Carlo study of scaling exponents of rough surfaces and correlated percolation
We calculate the scaling exponents of the two-dimensional correlated
percolation cluster's hull and unscreened perimeter. Correlations are
introduced through an underlying correlated random potential, which is used to
define the state of bonds of a two-dimensional bond percolation model.
Monte-Carlo simulations are run and the values of the scaling exponents are
determined as functions of the Hurst exponent H in the range -0.75 <= H <= 1.
The results confirm the conjectures of earlier studies
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
Effective Field Theory of Triangular-Lattice Three-Spin Interaction Model
We discuss an effective field theory of a triangular-lattice three-spin
interaction model defined by the variables. Based on the
symmetry properties and the ideal-state graph concept, we show that the vector
dual sine-Gordon model describes the long-distance properties for ; we
then compare its predictions with the previous argument. To provide the
evidences, we numerically analyze the eigenvalue structure of the transfer
matrix for , and we check the criticality with the central charge of
the intermediate phase and the quantization condition of the vector charges.Comment: 4 pages, 3 figure
Roughening Induced Deconstruction in (100) Facets of CsCl Type Crystals
The staggered 6-vertex model describes the competition between surface
roughening and reconstruction in (100) facets of CsCl type crystals. Its phase
diagram does not have the expected generic structure, due to the presence of a
fully-packed loop-gas line. We prove that the reconstruction and roughening
transitions cannot cross nor merge with this loop-gas line if these degrees of
freedom interact weakly. However, our numerical finite size scaling analysis
shows that the two critical lines merge along the loop-gas line, with strong
coupling scaling properties. The central charge is much larger than 1.5 and
roughening takes place at a surface roughness much larger than the conventional
universal value. It seems that additional fluctuations become critical
simultaneously.Comment: 31 pages, 9 figure
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