Related papers: Discrete JT gravity as an Ising model
The two-dimensional Ising model is studied at the boundary of a half-infinite cylinder. The three regular lattices (square, triangular and hexagonal) and the three regimes (sub-, super- and critical) are discussed. The probability of having…
We study the gravitational edge modes (GrEMs) and gauge edge modes (GaEMs) in Jackiw-Teitelboim (JT) gravity on a wiggling boundary. The wiggling effect manifests as a series of spacetime topological and bulk constraints for both conical…
We study a higher-order Painlev\'{e}-type equation, arising as a string equation of the $3^{rd}$ order reduction of the KP hierarchy. This equation appears at the multi-critical point of the $2$-matrix model with quartic interactions, and…
This is the second in a series of three articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling limit of the critical Ising model in slit-strip geometry. Here we study the fusion…
Some recently proposed definitions of Jackiw-Teitelboim gravity and supergravities in terms of combinations of minimal string models are explored, with a focus on physics beyond the perturbative expansion in spacetime topology. While this…
We consider three-dimensional Einstein gravity in Euclidean signature with a finite boundary of torus topology endowed with an induced metric of fixed conformal class and a constant trace of extrinsic curvature $K$. For vanishing, positive,…
We study the critical Ising model with free boundary conditions on finite domains in $\mathbb{Z}^d$ with $d\geq4$. Under the assumption, so far only proved completely for high $d$, that the critical infinite volume two-point function is of…
We give further evidence that the matrix-tensor model studied in \cite{belin2023} is dual to AdS$_{3}$ gravity including the sum over topologies. This provides a 3D version of the duality between JT gravity and an ensemble of random…
We show that two-dimensional JT gravity, the holographic dual of the IR fixed point of the SYK model, can be obtained from the consistent Kaluza-Klein reduction of a class of EMD theories in general $D$ dimensions. For $D=4$, $5$, the EMD…
We analyze boundary spin correlation functions of the hyperbolic-lattice Ising model from the holographic point of view. Using the corner-transfer-matrix renormalization group (CTMRG) method, we demonstrate that the boundary correlation…
In this note, we consider the asymmetric nearest neighbor ferromagnetic Ising model on the $(d+s)$-dimensional unit cubic lattice $\Z^{d+s}$, at inverse temperature $\beta=1$ and with coupling constants $J_s>0$ and $J_d>0$ for edges of…
Recent developments in topological mechanics have demonstrated the ability of Maxwell lattices to effectively focus stress along domain walls between differently polarized domains. The focusing ability can be exploited to protect the…
We provide a framework to study the interfaces imposed by Dobrushin boundary conditions on the half-plane version of the Ising model on random triangulations with spins on vertices. Using the combinatorial solution by Albenque, M\'enard and…
We study the gravitational edge mode in the $\mathcal{N}=1$ Jackiw-Teitelboim~(JT) supergravity on the disk and it $osp(2|1)$ BF formulation. We revisit the derivation of the finite-temperature Schwarzian action in the conformal gauge of…
Lattice gauge theory with gauge group $Z_{P}$ is reconsidered in four dimensions on a simplicial complex $K$. One finds that the dual theory, formulated on the dual block complex $\hat{K}$, contains topological modes which are in…
Using Monte Carlo techniques, Ising models with ferromagnetic nearest-neighbor interactions on a simple cubic lattice are studied. At the surface transition, the critical exponent $\beta_2$ of the edge magnetization is found to be…
A model describing Ising spins with short range interactions moving randomly in a plane is considered. In the presence of a hard core repulsion, which prevents the Ising spins from overlapping, the model is analogous to a dynamically…
We investigate constraints imposed by entanglement on gravity in the context of holography. First, by demanding that relative entropy is positive and using the Ryu-Takayanagi entropy functional, we find certain constraints at a nonlinear…
We propose a new, discretized model for the study of 3+1-dimensional canonical quantum gravity, based on the classical $SL(2,\C)$-connection formulation. The discretization takes place on a topological $N^3$- lattice with periodic boundary…
This thesis is driven by a central question: "What can we learn from random geometries about the structure of quantum spacetime?" In Chapter 2, we provide a partial review of the mathematical foundation of this thesis, random geometry. In…