Related papers: Ising on $\mathbb{S}^2$ -- The Affine Conjecture
The effective action of the SU(N) Polyakov loop model in the strong coupling region and in the static limit for the quark determinant can be mapped onto the Ising model in any dimensions, with the Ising variables attached on the links of…
We study the 1d Ising model with long-range interactions decaying as $1/r^{1+s}$. The critical model corresponds to a family of 1d conformal field theories (CFTs) whose data depends nontrivially on $s$ in the range $1/2\leq s\leq 1$. The…
We present a characterization of the many-body lattice wave functions obtained from the conformal blocks (CBs) of the Ising conformal field theory (CFT). The formalism is interpreted as a matrix product state using continuous ancillary…
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…
In 1980 Jimbo and Miwa evaluated the diagonal two-point correlation function of the square lattice Ising model as a $\tau$-function of the sixth Painlev\'e system by constructing an associated isomonodromic system within their theory of…
A notion of effective gauge fields which does not involve a background metric is introduced. The role of scale is played by cellular decompositions of the base manifold. Once a cellular decomposition is chosen, the corresponding space of…
Two triangle meshes are conformally equivalent if for any pair of incident triangles the absolute values of the corresponding cross-ratios of the four vertices agree. Such a pair can be considered as preimage and image of a discrete…
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…
The qualitative aspects of the phase diagram of the Ising model on the cubic lattice, with ferromagnetic nearest-neighbor interactions ($J_{1}$) and antiferromagnetic next-nearest-neighbor couplings ($J_{2}$) are analyzed in the plane…
We formulate the conformal mapping between $R^3$ and $S^3$, the 3 sphere. This mapping is applied to the critical Ising model. From this mapping, we calculate the second and fourth moments of the magnetization density, and using those…
The 3d Ising model in the low temperature (ferromagnetic) phase describes dynamics of two-dimensional surfaces -- domain walls between clusters of parallel spins. The Kramers--Wannier duality maps these surfaces into worldsheets of…
We study the flux tube thickness in the confining phase of the (2+1)d SU(2) Lattice Gauge Theory near the deconfining phase transition. Following the Svetitsky-Yaffe conjecture, we map the problem to the study of the <epsilon sigma sigma>…
An asymmetrical 2D Ising model with a zigzag surface, created by diagonally cutting a regular square lattice, has been developed to investigate the thermodynamics and phase transitions on surface by the methodology of recursive lattice,…
We analyze the ground state phase diagram of attractive lattice bosons, which are stabilized by a three-body onsite hardcore constraint. A salient feature of this model is an Ising type transition from a conventional atomic superfluid to a…
We study connection probabilities between vertices of the square lattice for the critical random-cluster (FK) model with cluster weight 2, which is related to the critical Ising model. We consider the model on the plane and on domains…
We construct a two-dimensional (2D) lattice model that is argued to realize a gapped chiral spin liquid with (Ising) non-Abelian topological order. The building blocks are spin-1/2 two-leg ladders with $SU(2)$-symmetric spin-spin…
Wegner duality is essential for Z2 lattice gauge theory, yet the duality on non-trivial topologies has remained implicit. We extend Wegner duality to arbitrary topology and dimension, obtaining a new class of Ising models, in which topology…
The correlation function of two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor representation are…
We perform Monte-Carlo simulations of the three-dimensional Ising model at the critical temperature and zero magnetic field. We simulate the system in a ball with free boundary conditions on the two dimensional spherical boundary. Our…
We study scalar conformal field theories whose large $N$ spectrum is fixed by the operator dimensions of either Ising model or Lee-Yang edge singularity. Using numerical bootstrap to study CFTs with $S_N\otimes Z_2$ symmetry, we find a…