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 ${\mathbb Z}_p$ 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 $p\ge5$; we then compare its predictions with the previous argument. To provide the evidences, we numerically analyze the eigenvalue structure of the transfer matrix for $p=6$, and we check the criticality with the central charge $c=2$ 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