Related papers: A dilogarithmic 3-dimensional Ising tetrahedron
We built a model where all spins are in interaction with each other via an antiferromagnetic Ising Hamiltonian. The geometry of such a model is a tetrahedron placed on a hypersphere in spaces of dimensions enclosed between 1 and 9. Due to…
The Ising model in two dimensions with special toroidal boundary conditions is analyzed. These boundary condition, which we call duality twisted boundary conditions, may be interpreted as inserting a specific defect line ("seam") in the…
We show how the Onsager algebra, used in the original solution of the two-dimensional Ising model, arises as an infinite-dimensional symmetry of certain self-dual models that also have a $U(1)$ symmetry. We describe in detail the example of…
We implement the conformal bootstrap program for three-dimensional CFTs with $\mathcal{N}=2$ supersymmetry and find universal constraints on the spectrum of operator dimensions in these theories. By studying the bounds on the dimension of…
The $N=\infty$ vector $O(N)$ model is a solvable, interacting field theory in three dimensions ($D$). In a recent paper with A. Chubukov and J. Ye~\cite{self}, we have computed a universal number, $\tilde{c}$, characterizing the size…
Ising spin glass models with bimodal, Gaussian, uniform and Laplacian interaction distributions in dimension five are studied through detailed numerical simulations. The data are analyzed in both the finite-size scaling regime and the…
Let $\varepsilon>0$. We construct an explicit, full-measure set of $\alpha \in[0,1]$ such that if $\gamma \in \mathbb{R}$ then, for almost all $\beta \in[0,1]$, if $\delta \in \mathbb{R}$ then there are infinitely many integers $n\geq 1$…
Extracting momentum-resolved excitation spectra in strongly correlated quantum systems remains a major challenge, especially beyond one spatial dimension. We present an efficient tensor-network approach to compute dispersion relations via…
We show that the two dimensional Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all…
This paper explores formalizing Geometric (or Clifford) algebras into the Lean 3 theorem prover, building upon the substantial body of work that is the Lean mathematics library, mathlib. As we use Lean source code to demonstrate many of our…
We propose a general method for the numerical evaluation of OPE coefficients in three dimensional Conformal Field Theories based on the study of the conformal perturbation of two point functions in the vicinity of the critical point. We…
We propose a solution to the puzzle of dimensional reduction in the random field Ising model, inverting the question and asking: to what random problem in $D=d+2$ dimensions does a pure system in $d$ dimensions correspond? We consider two…
If the four triangular facets of a tetrahedron can be partitioned into pairs having the same area, then the triangles in each pair must be congruent to one another. A Heron-style formula is then derived for the volume of a tetrahedron…
We demonstrate, by means of a convolutional neural network, that the features learned in the two-dimensional Ising model are sufficiently universal to predict the structure of symmetry-breaking phase transitions in considered systems…
In this study, we computed three critical exponents ($\alpha, \beta, \gamma$) for the 3D Ising model with Metropolis Algorithm using Finite-Size Scaling Analysis on six cube length scales (L=20,30,40,60,80,90), and performed a supervised…
We study universality in three-dimensional Ising spin glasses by large-scale Monte Carlo simulations of the Edwards-Anderson Ising spin glass for several choices of bond distributions, with particular emphasis on Gaussian and bimodal…
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…
Recently Terwilliger and the present author found a presentation for the three-point $\mathfrak{sl}_2$ loop algebra via generators and relations. To obtain this presentation we defined a Lie algebra $\boxtimes$ by generators and relations…
To gain a better understanding of the interplay between frustrated long-range interactions and zero-temperature quantum fluctuations, we investigate the ground-state phase diagram of the transverse-field Ising model with…
A triangular limit algebra A is isometrically isomorphic to the tensor algebra of a C*-correspondence if and only if its fundamental relation R(A) is a tree admitting a $Z^+_0$-valued continuous and coherent cocycle. For triangular limit…