Related papers: Thin Absolute Villains
The nearest-neighbor Villain, or periodic Gaussian, model is a useful tool to understand the physics of the topological defects of the two-dimensional nearest-neighbor $XY$ model, as the two models share the same symmetries and are in the…
We consider a soluble model of large $\phi^{4}$-graphs randomly embedded in one compactified dimension; namely the large-order behaviour of finite-temperature perturbation theory for the partition function of the anharmonic oscillator. We…
We investigate numerically and analytically Potts models on ``thin'' random graphs -- generic Feynman diagrams, using the idea that such models may be expressed as the N --> 1 limit of a matrix model. The thin random graphs in this limit…
Exact and/or rigorous results are reviewed for the Ising and XY/Villain spin glasses in finite dimensions, such as the exact energy, correlation identities and a functional relation between the distribution functions of ferromagnetic and…
Worm methods to simulate the Ising model in the Aizenman random current representation including a low noise estimator for the connected four point function are extended to allow for antiperiodic boundary conditions. In this setup several…
We report precise simulations of phi^4 theory in the Ising limit. A recent technique to stochastically evaluate the all-order strong coupling expansion is combined with exact identities in the closely related Aizenman random current…
We address the question of the order of the deconfinement phase transition of four dimensional U(1) lattice gauge theory. Simulations of the Z-gauge theory dual to the Villain action on toroidal lattices up to lattice sizes of 28^4 give…
We simulate the 2d U(1) gauge Higgs model on the lattice with a topological angle $\theta$. The corresponding complex action problem is overcome by using a dual representation based on the Villain action appropriately endowed with a…
The ground state and low T behavior of two-dimensional spin systems with discrete binary couplings are subtle but can be analyzed using exact computations of finite volume partition functions. We first apply this approach to Villain's fully…
We investigate the Yang-Lee edge singularity on non-planar random graphs, which we consider as the Feynman Diagrams of various d=0 field theories, in order to determine the value of the edge exponent. We consider the hard dimer model on…
Using 2-d U(1) lattice gauge theory we study two definitions of the topological charge constructed from a generalized Villain action and analyze the implementation of the index theorem based on the overlap Dirac operator. One of the two…
We study a general class of nonlinear iterative algorithms which includes power iteration, belief propagation and approximate message passing, and many forms of gradient descent. When the input is a random matrix with i.i.d. entries, we use…
We prove that the theory of the Farey graph is pseudofinite by constructing a sequence of finite structures that satisfy increasingly large subsets of its first-order axiomatization. This graph is an important object in the study of curve…
Scalar field theories with quartic interactions are of central interest in the study of second-order phase transitions. For three-dimensional theories, numerous studies make use of the fixed-dimensional perturbative computation of [B.…
We consider extremal problems for subgraphs of pseudorandom graphs. For graphs $F$ and $\Gamma$ the generalized Tur\'an density $\pi_F(\Gamma)$ denotes the density of a maximum subgraph of $\Gamma$, which contains no copy of~$F$. Extending…
The Cardy-Rabinovici model is a toy model of the lattice $U(1)$ gauge theories to study various oblique confinement states associated with the nonzero $\theta$ angles. We reformulate the $2$d version of this model using the modified Villain…
We carry out simulations of the anisotropic uniformly frustrated 3D XY model, as a model for vortex line fluctuations in high Tc superconductors. We compute the phase diagram as a function of temperature and anisotropy, for a fixed applied…
The non-compact lattice version of the Abelian Higgs model is studied in terms of its topological excitations. The Villain form of the partition function is represented as a sum over world-sheets of gauge-invariant ``vortex'' strings. The…
We consider a spin-$\frac{1}{2}$ chain with competing nearest and next-nearest neighbor interactions within a transverse magnetic field, which is known to be an equiavelent to the ANNNI model. When studing thermodynamics of the 2D ANNNI…
In the linear-in-means model, endogeneity arises naturally due to the reflection problem. A common solution is to use Instrumental Variables (IVs) based on higher-order network links, such as using friends-of-friends' characteristics. We…