Related papers: Simplicial Lattice Study of the 2d Ising CFT
The partition function of the two-dimensional Ising model is exactly obtained on a lattice with a twisted boundary condition. The continuum limit of the model off the critical temperature is found to give the mass-deformed Ising conformal…
To investigate the properties of $c=1$ matter coupled to $2$d{--}gravity we have performed large-scale simulations of two copies of the Ising Model on a dynamical lattice. We measure spin susceptibility and percolation critical exponents…
We propose a method to study the second-order critical lines of classical spin-$S$ Ising models on two-dimensional lattices in a crystal or splitting field, using an exact expression for the bare mass of the underlying field theory.…
We formulate a non-perturbative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a causal structure. The model can be solved exactly at the discretized level. Its continuum…
Lattice radial quantization is introduced as a nonperturbative method intended to numerically solve Euclidean conformal field theories that can be realized as fixed points of known Lagrangians. As an example, we employ a lattice shaped as a…
We study mappings between distinct classical spin systems that leave the partition function invariant. As recently shown in [Phys. Rev. Lett. 100, 110501 (2008)], the partition function of the 2D square lattice Ising model in the presence…
Regge calculus is a powerful method to approximate a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The discrete Regge model…
We report a high statistics simulation of Ising spins coupled to 2D quantum gravity in the Regge calculus approach using triangulated tori with up to $512^2$ vertices. For the constant area ensemble and the $dl/l$ functional measure we…
We investigate the critical behaviour of the two-dimensional Ising model defined on a curved surface with a constant negative curvature. Finite-size scaling analysis reveals that the critical exponents for the zero-field magnetic…
A new realization of the conformal algebra is studied which mimics the behaviour of a statistical system on a discrete albeit infinite lattice. The two-point function is found from the requirement that it transforms covariantly under this…
We provide compelling evidence that a previously introduced model of non-perturbative 2d Lorentzian quantum gravity exhibits (two-dimensional) flat-space behaviour when coupled to Ising spins. The evidence comes from both a high-temperature…
It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no mathematical proof of universality and conformal…
A simple d-dimensional lattice model is proposed, incorporating some degree of frustration and thus capable of describing some aspects of molecular orientation in covalently bound molecular solids. For d=2 the model is shown to be…
Aiming at the study of critical phenomena in the presence of boundaries with a non-trivial shape we discuss how lattices with an adaptive lattice spacing can be implemented. Since the parameters of the Hamiltonian transform non-trivially…
In this paper we investigate the nature of the singularity of the Ising model of the 4-dimensional cubic lattice. It is rigorously known that the specific heat has critical exponent $\alpha=0$ but a non-rigorous field-theory argument…
The finite lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the spin-1 Ising model on the square lattice. A new formalism is described that…
We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices with up to 80,000 sites which are linked together according to the Voronoi/Delaunay prescription. In one set of…
We review some aspects of the fermionic interpretation of the two-dimensional Ising model. The use is made of the notion of the integral over the anticommuting Grassmann variables. For simple and more complicated 2D Ising lattices, the…
Topological defects play a fundamental role in the investigation of symmetries in quantum field theories. For conformal field theories in two space-time dimensions, it is possible to construct these defects using lattice models allowing…
We study the zeros in the complex plane of the partition function for the Ising model coupled to 2d quantum gravity for complex magnetic field and real temperature, and for complex temperature and real magnetic field, respectively. We…