The exact vanishing of the interaction corrections to zero temperature and frequency conductivity graphene in presence weak short range interactions is rigorously established.

We consider a class of non-integrable 2D Ising models obtained by perturbing the nearest-neighbor model via weak, finite range potential which preserves translation and spin-flip symmetry, we study its critical theory in half-plane. prove that leading order long-distance behavior correlation functions for spins on boundary is same as model, up to an analytic multiplicative renormalization constant. In particular, scaling limit Pfaffian explicit matrix. The proof based exact representation...

We consider a non-integrable model for interacting dimers on the two-dimensional square lattice. Configurations are perfect matchings of $\mathbb Z^2$, i.e. subsets edges such that each vertex is covered exactly once ("close-packing" condition). Dimer configurations in bijection with discrete height functions, defined faces $\boldsymbol{\xi}$ Z^2$. The non-interacting "integrable" and solvable via Kasteleyn theory; it known all moments difference $h_{\boldsymbol{\xi}}-h_{\boldsymbol{\eta}}$...

Abstract We study a class of close-packed dimer models on the square lattice, in presence small but extensive perturbations that make them non-determinantal. Examples include 6-vertex model close to free-fermion point, and with plaquette interaction previously analyzed previous works. By tuning edge weights, we can impose non-zero average tilt for height function, so considered are general not symmetric under discrete rotations reflections. In determinantal case, fluctuations massless (or...

Much of our understanding critical phenomena is based on the notion Renormalization Group (RG), but actual determination its fixed points usually approximations and truncations, predictions physical quantities are often limited accuracy. The RG can be however given a fully rigorous non-perturbative characterization, this what presented here in model symplectic fermions with nonlocal ("long-range") kinetic term depending parameter $\varepsilon$ quartic interaction. We identify Banach space...

A study of substrate removal by real activated sludge with several synthetic substrates (acetate, ethanol, glutamic acid) and wastewater (raw filtered) was carried out. Substrate, stored compounds (polyhydroxyalkanoates, PHA internal carbohydrates), ammonia oxygen uptake rate (OUR) were analytically determined. Polyhydroxybutyrate (PHB) when the acetate or while no appreciable formation storage compound detected using acid. low amount PHB also formed in tests raw filtered which probably...

We study the ground state of a $d$-dimensional Ising model with both long-range (dipole-like) and nearest-neighbor ferromagnetic (FM) interactions. The interaction is equal to ${r}^{\ensuremath{-}p}$, $p>d$, while FM has strength $J$. If $p>d+1$ $J$ large enough FM, if $d<p\ensuremath{\leqslant}d+1$ not for any choice In $d=1$ we show that $p>1$ series transitions from an antiferromagnetic period 2 $2h$-periodic states blocks sizes $h$ alternating sign, size growing when...

We consider Ising models in two and three dimensions, with short range ferromagnetic long range, power-law decaying, antiferromagnetic interactions. let J be the ratio between strength of to The competition these kinds interactions induces system form domains minus spins a background plus spins, or vice versa. If decay exponent p interaction is larger than d + 1, space dimension, this happens for all values smaller critical value c (p), beyond which ground state homogeneous. In paper, we...

We study the zero-temperature phase diagram of Ising spin systems in two dimensions presence competing interactions: long-range antiferromagnetic and nearest-neighbor ferromagnetic strength $J$. first introduce notion a ``corner energy,'' which shows, when interaction decays faster than fourth power distance, that striped state is favored with respect to checkerboard $J$ close ${J}_{c}$, transition state, i.e., length scales uniformly magnetized domains become large. Next, we perform...

We consider a class of non-integrable 2D Ising models, whose Hamiltonian, in addition to the nearest neighbor couplings, includes weak multi-spin interactions, even under spin flip. study model cylindrical domains arbitrary aspect ratio and prove that, scaling limit, multipoint energy correlations converge same limiting as those nearest-neighbor cylinder with renormalized up an overall multiplicative constant, independent shape size domain. The proof is based on representation generating...

We prove that a system of discrete 2D in-plane dipoles with four possible orientations, interacting via 3D dipole-dipole interaction plus nearest neighbor ferromagnetic term, has periodic striped ground states. As the strength term is increased, size stripes in state increases, becoming infinite, i.e., giving ferromagentic state, when exceeds certain critical value. also give rigorous proof reorientation transition six antiferromagnetic term. increased flips from being and to staggered...

The effects of the electromagnetic (em) electron-electron interactions in half-filled graphene are investigated terms a lattice gauge theory model. By using exact renormalization group methods and Ward identities, we show that em amplify responses to excitonic pairings associated Kekul\'e distortion charge-density wave. effect electronic repulsion on Peierls-Kekul\'e instability, usually neglected, is evaluated by deriving an non BCS gap equation, from which find evidence strong among...

We obtain an explicit expression for the multipoint energy correlations of a non-solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus weak finite range interaction strength λ, in scaling limit which we send lattice spacing to zero and temperature critical one. Our analysis is based on exact mapping model into interacting fermionic theory, generalizes one originally used by Schultz, Mattis, Lieb model. The then analyzed multiscale method first proposed...

We consider the two-dimensional Hubbard model on honeycomb lattice, as a for single-layer graphene with screened Coulomb interactions; at half filling and weak coupling, we construct its ground-state correlations by convergent multiscale expansion, rigorously excluding presence of magnetic or superconducting instabilities formation mass gap. The Fermi velocity, which can be written in terms series remains close to noninteracting value turns out isotropic; consequence, Dirac cones are...