Research output: Contribution to conference › Paper

Abstract

The 6-vertex F model on the square lattice exhibits a critical line with central chargeC = 1, terminating
in a critical point of the Kosterlitz-Thouless type. As such, its coupling to two-dimensional
quantum gravity by placing it onto the dynamically triangulated random surfaces (DTRS) of the
simplicial formulation yields an interesting realization of the limiting case C = 1 where the continuum
description of quantum gravity plus matter fields in two dimensions breaks down. Technically,
since the general 6- and 8-vertex models of statistical mechanics are defined with respect
to four-valent lattices, the model has to be coupled to dynamical quadrangulations. Generalizing
the well-known algorithmic tools for treating dynamical triangulations in a Monte Carlo simulation
to the case of these random lattices made of squares, we present extensive numerical results
for the critical-point properties of the coupled system, including the matter related as well as the
graph related critical exponents of the model.

title = "Simulations of the F model on planar φ 4 Feynman diagrams",

abstract = "The 6-vertex F model on the square lattice exhibits a critical line with central chargeC = 1, terminating in a critical point of the Kosterlitz-Thouless type. As such, its coupling to two-dimensional quantum gravity by placing it onto the dynamically triangulated random surfaces (DTRS) of the simplicial formulation yields an interesting realization of the limiting case C = 1 where the continuum description of quantum gravity plus matter fields in two dimensions breaks down. Technically, since the general 6- and 8-vertex models of statistical mechanics are defined with respect to four-valent lattices, the model has to be coupled to dynamical quadrangulations. Generalizing the well-known algorithmic tools for treating dynamical triangulations in a Monte Carlo simulation to the case of these random lattices made of squares, we present extensive numerical results for the critical-point properties of the coupled system, including the matter related as well as the graph related critical exponents of the model.",

author = "Wolfhard Janke and Martin Weigel",

note = "The full text is available from: http://pos.sissa.it/archive/conferences/020/251/LAT2005_251.pdf; XXXLII International Symposium on Lattice Field Theory and Statistical Physics ; Conference date: 25-07-2005 Through 30-07-2005",

year = "2005",

language = "English",

}

TY - CONF

T1 - Simulations of the F model on planar φ 4 Feynman diagrams

AU - Janke, Wolfhard

AU - Weigel, Martin

N1 - The full text is available from: http://pos.sissa.it/archive/conferences/020/251/LAT2005_251.pdf

PY - 2005

Y1 - 2005

N2 - The 6-vertex F model on the square lattice exhibits a critical line with central chargeC = 1, terminating
in a critical point of the Kosterlitz-Thouless type. As such, its coupling to two-dimensional
quantum gravity by placing it onto the dynamically triangulated random surfaces (DTRS) of the
simplicial formulation yields an interesting realization of the limiting case C = 1 where the continuum
description of quantum gravity plus matter fields in two dimensions breaks down. Technically,
since the general 6- and 8-vertex models of statistical mechanics are defined with respect
to four-valent lattices, the model has to be coupled to dynamical quadrangulations. Generalizing
the well-known algorithmic tools for treating dynamical triangulations in a Monte Carlo simulation
to the case of these random lattices made of squares, we present extensive numerical results
for the critical-point properties of the coupled system, including the matter related as well as the
graph related critical exponents of the model.

AB - The 6-vertex F model on the square lattice exhibits a critical line with central chargeC = 1, terminating
in a critical point of the Kosterlitz-Thouless type. As such, its coupling to two-dimensional
quantum gravity by placing it onto the dynamically triangulated random surfaces (DTRS) of the
simplicial formulation yields an interesting realization of the limiting case C = 1 where the continuum
description of quantum gravity plus matter fields in two dimensions breaks down. Technically,
since the general 6- and 8-vertex models of statistical mechanics are defined with respect
to four-valent lattices, the model has to be coupled to dynamical quadrangulations. Generalizing
the well-known algorithmic tools for treating dynamical triangulations in a Monte Carlo simulation
to the case of these random lattices made of squares, we present extensive numerical results
for the critical-point properties of the coupled system, including the matter related as well as the
graph related critical exponents of the model.