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We show that, independently of the boundary conditions, the two phases of the 4-dimensional compact U(1) lattice gauge theory can be characterized by the presence or absence of an ``infinite'' current network, with an appropriate definition…
Some time ago Salmhofer demonstrated the equivalence of the strong coupling lattice Schwinger model with Wilson fermions to a certain 8-vertex model which can be understood as a self-avoiding loop model on the square lattice with bending…
We study the phase diagram of a system of $2\times 2\times 1$ hard plates on the three dimensional cubic lattice, {\em i.e.} a lattice gas of plates that each cover an elementary plaquette of the cubic lattice and occupy its four vertices,…
Quantum link models are extensions of Wilson-type lattice gauge theories which realize exact gauge invariance with finite-dimensional Hilbert spaces. Quantum link models not only reproduce the standard features of Wilson's lattice gauge…
A lattice quantum gravity model in 4 dimensional Riemannian spacetime is constructed based on the SU(2) Ashtekar formulation of general relativity. This model can be understood as one of the family of models sometimes called ``spin foam…
We investigate the Z(2) gauge model on a generalized Bethe lattice with three plaquette representation of the action. We obtain the cascade of phase transitions according to Feigenbaum scheme leading to chaotic states for some values of…
We study the U(2) lattice gauge theory in the pure gauge sector using the simplest action, with determinant and fundamental terms, having the naive continuum limit of SU(2)$\times$U(1). We determine part of the phase diagram of the model…
Lattice systems with certain Lie algebraic or quantum Lie algebraic symmetries are constructed. These symmetric models give rise to series of integrable systems. As examples the $A_n$-symmetric chain models and the SU(2)-invariant ladder…
A phase transition for bosonic atoms in a two-dimensional anisotropic optical lattice is considered. If the tunnelling rates in two directions are different, the system can undergo a transition between a two-dimensional superfluid and a…
We numerically investigate the multicritical behavior of the three dimensional lattice system in which a SU(2) gauge field is coupled to two flavors of scalar fields transforming in the fundamental representation of the gauge group. In this…
Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior and universality for the isotropic-nematic phase transition in a system of long straight rigid rods of length $k$ ($k$-mers) on…
We use a scattering formalism to derive a condition of strong coupling between a resonant scatterer and an Anderson localized mode for electromagnetic waves in two dimensions. The strong coupling regime is demonstrated based on exact…
We spell out the derivation of novel features, put forward earlier in a letter, of two dimensional gravity in the strong coupling regime, at $C_L=7$, 13, 19. Within the operator approach previously developed, they neatly follow from the…
We show that the two phases of the 4-dimensional compact U(1) lattice gauge theory are characterized by the existence or absence of an infinite current network, defining ``infinite'' on a finite lattice in a manner appropriate to the chosen…
A systematic method to obtain strong coupling expansions for scattering quantities in Hamiltonian lattice field theories is presented. I develop the conceptual ideas by means of the Hamiltonian field theory analogue of the Ising model, in…
We investigate the critical properties of the spin-3/2 Blume-Capel model in two dimensions on a random lattice with quenched connectivity disorder. The disordered system is simulated by applying the cluster hybrid Monte Carlo update…
We introduce a deterministic SO(3) invariant dynamics of classical spins on a discrete space-time lattice and prove its complete integrability by explicitly finding a related non-constant (baxterized) solution of the set-theoretic quantum…
The phase ordering kinetics of the two-dimensional uniaxial nematic has been studied using a Cell Dynamic Scheme. The system after quench from T=infinity was found to scale dynamically with an asymptotic growth law similar to that of…
It was recently proposed in https://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.043322 [Herdeiro & Doyon Phys.,Rev.,E (2016)] a numerical method showing a precise sampling of the infinite plane 2d critical Ising model for finite…
Let $\mathcal{B}$ be a compact convex planar domain with smooth boundary of finite type and $\mathcal{B}_\theta$ its rotation by an angle $\theta$. We prove that for almost every $\theta\in[0, 2\pi]$ the remainder…