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We study a two-parameter family of quantum spin systems on the complete graph, which is the most general model invariant under the complex orthogonal group. In spin $S=\frac{1}{2}$ it is equivalent to the XXZ model, and in spin $S=1$ to the…
We revisit the problem of building consistent interactions for a multiplet of partially massless spin-2 fields in (anti-)de Sitter space. After rederiving and strengthening the existing no-go result on the impossibility of Yang-Mills type…
In the dimer model, a configuration consists of a perfect matching of a fixed graph. If the underlying graph is planar and bipartite, such a configuration is associated to a height function. For appropriate "critical" (weighted) graphs,…
We derive the self-consistent harmonic approximation for the $2D$ XY model with non-local interactions. The resulting equation for the variational couplings holds for any form of the spin-spin coupling as well as for any dimension. Our…
Motivated by recent progress on synthesizing two-dimensional magnetic van der Waals systems, we propose a setup for detecting the topological Berezinskii-Kosterlitz-Thouless (BKT) phase transition in spin-transport experiments on such…
Phase diagram, critical properties and thermodynamic functions of the two-dimensional field-free quantum-spin-1/2 XXZ model has been calculated globally using a numerical renormalization group theory. The nearest-neighbor spin-spin…
Using the parent Lagrangian method together with a dimensional reduction from $D$ to $(D-1)$ dimensions we construct dual theories for massive spin two fields in arbitrary dimensions in terms of a mixed symmetry tensor $T_{A[A_{1}A_{2}...…
We address here a few classical lattice--spin models, involving $n-$component unit vectors ($n=2,3$), associated with a $D-$dimensional lattice $\mathbb{Z}^D,\,D=1,2$, and interacting via a pair potential restricted to nearest neighbours…
Holographic duality is argued to relate classes of models that have equivalent unfolded formulation, hence exhibiting different space-time visualizations for the same theory. This general phenomenon is illustrated by the $AdS_4$ higher-spin…
We study three dimensional O(N)_k and U(N)_k Chern-Simons theories coupled to a scalar field in the fundamental representation, in the large N limit. For infinite k this is just the singlet sector of the O(N) (U(N)) vector model, which is…
The large spacing phase of the infinite random matrix chain, which represents the strongly coupled two-dimensional O(2) model on a random planar lattice, is explored. A class of solutions valid for large lattice spacings is constructed. It…
We computed potentials between static color sources from the six lowest representations of G(2) lattice gauge theory, in numerical simulations with the Wilson action on asymmetric lattices with nonperturbatively estimated values of the bare…
Fathoming deconfined phases is one of the key issues in modern condensed matter. Striking many-body effects including massive quantum entanglement and coherence may be realized as manifested in quantum spin liquids and topological orders.…
In our recent paper we described relationships between integrable systems inspired by the AGT conjecture. On the gauge theory side an integrable spin chain naturally emerges while on the conformal field theory side one obtains some special…
The solid-on-solid model is a model of height functions, introduced to study the interface separating the $+$ and $-$ phase in the Ising model. The planar solid-on-solid model thus corresponds to the three-dimensional Ising model.…
We study the large-scale behavior of the height function in the dimer model on the square lattice. Richard Kenyon has shown that the fluctuations of the height function on Temperleyan discretizations of a planar domain converge in the…
This is the second paper in the series devoted to the study of the dimer model on t-embeddings of planar bipartite graphs. We introduce the notion of perfect t-embeddings and assume that the graphs of the associated origami maps converge to…
Two-dimensional BF theory with infinitely many higher spin fields is proposed. It is interpreted as the AdS(2) higher spin gravity model describing a consistent interaction between local fields in AdS(2) space including gravitational field,…
We consider the finite-temperature frequency and momentum dependent two-point functions of local operators in integrable quantum field theories. We focus on the case where the zero temperature correlation function is dominated by a…
We study gapless quantum spin chains with spin 1/2 and 1: the Fredkin and Motzkin models. Their entangled groundstates are known exactly but not their excitation spectra. We first express the groundstates in the continuum which allows for…