相关论文: A note on the 3D Ising model as a string theory

We propose a lattice field theory formulation which overcomes some fundamental difficulties in realizing exact supersymmetry on the lattice. The Leibniz rule for the difference operator can be recovered by defining a new product on the…

There has been much recent interest devoted to a class of frustrated one-dimensional statistical mechanics lattice models which exhibit sharp thermodynamics. In this work, we study an extension of one of these models to two dimensions; the…

The spin - 3/2 Ising model on a square lattice is investigated. It is shown that this model is reducible to an eight - vertex model on a surface in the parameter space spanned by coupling constants J, K, L and M. It is shown that this model…

We suggest a conformally invariant generalization of string theory to higher-dimensional objects. As such a model, we consider a conformally invariant $\sigma$ model. For this theory, the Hamiltonian formalism is constructed, and the full…

Motivated by recent interest in 2+1 dimensional quantum dimer models, we revisit Fisher's mapping of two dimensional Ising models to hardcore dimer models. First, we note that the symmetry breaking transition of the ferromagetic Ising model…

We demonstrate that the Ising model on a general triangular graph with 3 distinct couplings $K_1,K_2,K_3$ corresponds to an affine transformed conformal field theory (CFT). Full conformal invariance of the $c= 1/2$ minimal CFT is restored…

String theory in 4 dimensions has the unique feature that a topological term, the oriented self-intersection number, can be added to the usual action. It has been suggested that the corresponding theory of random surfaces wold be free from…

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…

We study the 2D Ising model on three different types of lattices that are topologically equivalent to spheres. The geometrical shapes are reminiscent of the surface of a pillow, a 3D cube and a sphere, respectively. Systems of volumes…

Form factor representation of the correlation function of the 2D Ising model on a cylinder is generalized to the case of arbitrary disposition of correlating spins. The magnetic susceptibility on a lattice, one of whose dimensions ($N$) is…

String field theory is a candidate for a full non-perturbative definition of string theory. We aim to define string field theory on a space-time lattice to investigate its behaviour at the quantum level. Specifically, we look at string…

We propose the use of lattice field theory for the study of string field theory at the non-perturbative quantum level. We identify many potential obstacles and examine possible resolutions thereof. We then experiment with our approach in…

How complex is an Ising model? Usually, this is measured by the computational complexity of its ground state energy problem. Yet, this complexity measure only distinguishes between planar and non-planar interaction graphs, and thus fails to…

The purpose of this article is to extend the lightcone worldsheet lattice description of string theory to include the Neveu-Schwarz model. We model each component of the fermionic worldsheet field by a critical Ising model. We show that a…

We discuss the classical continuum limit of the string field theory dual to the $\mathrm{SU}(N)$ lattice gauge theory and investigate various fundamental phenomena in the continuum theory at the mean-field level. Our construction of the…

In these lectures I discuss various unsolved problems of string theory and their relations to quantum gravity, 3d Ising model, large N QCD, and quantum cosmology. No solutions are presented but some new and perhaps useful approaches are…

The 3d Ising model on a regular cubic lattice can be expressed in terms of an SU(2) 2d fermionic model with a $Z_2$-fluxes. We modify the model such that it is defined on the dual to a body centered cubic lattice. The advantage of this…

After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…

A $d$-dimensional Ising model on a lattice torus is considered. As the size $n$ of the lattice tends to infinity, a Poisson approximation is given for the distribution of the number of copies in the lattice of any given local configuration,…

It is generally accepted that the double-scaled 1D matrix model is equivalent to the $c=1$ string theory with tachyon condensation. There remain however puzzles that are to be clarified in order to utilize this connection for our quest…