Exact solution of the six-vertex model on a random lattice

Abstract We solve exactly the 6-vertex model on a dynamical random lattice, using its representation as a large N matrix model. The model describes a gas of dense nonintersecting oriented loops coupled to the local curvature defects on the lattice. The model can be mapped to the c =1 string theory, compactified at some length depending on the vertex coupling. We give explicit expression for the disk amplitude and evaluate the fractal dimension of its boundary, the average number of loops and the dimensions of the vortex operators, which vary continuously with the vertex coupling.

[1]  Multicritical phases of the O(n) model on a random lattice , 1992, hep-th/9203030.

[2]  David P. Landau,et al.  Phase transitions and critical phenomena , 1989, Computing in Science & Engineering.

[3]  D. Gross,et al.  Nonperturbative two-dimensional quantum gravity. , 1990, Physical review letters.

[4]  P. Byrd,et al.  Handbook of Elliptic Integrals for Engineers and Physicists , 2014 .

[5]  Vladimir Kazakov,et al.  Recent progress in the theory of noncritical strings , 1988 .

[6]  R. Baxter.  Exactly solved models in statistical mechanics , 1982 .

[7]  Jens Hoppe,et al.  Quantum theory of a massless relativistic surface and a two-dimensional bound state problem , 1982 .

[8]  I. Kostov.  THE ADE FACE MODELS ON A FLUCTUATING PLANAR LATTICE , 1989 .

[9]  The O(n) model on a random surface: critical points and large-order behaviour , 1992, hep-th/9204082.

[10]  Strings with discrete target space , 1991, hep-th/9112059.

[11]  D. Gross,et al.  One-dimensional string theory on a circle , 1990 .

[12]  Exact solution of the O(n) model on a random lattice , 1995, hep-th/9506193.

[13]  P. Zinn-Justin,et al.  Two-matrix model with ABAB interaction , 1999 .

[14]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[15]  Edouard Brézin,et al.  Exactly Solvable Field Theories of Closed Strings , 1990 .

[16]  M. Gaudin,et al.  O(n) model on a fluctuating planar lattice. Some exact results , 1989 .

[17]  Michael R. Douglas,et al.  STRINGS IN LESS THAN ONE DIMENSION , 1990 .

[18]  B. Duplantier,et al.  Geometrical critical phenomena on a random surface of arbitrary genus , 1990 .