Related papers: Who told you magnetization is a vector in $4-\epsi…
Hierarchical renormalization group transformations are related to non-associative algebras. Non-trivial infrared fixed points are shown to be solutions of polynomial equations. At the example of a scalar model in $d(\ge2)$ dimensions some…
A K\"ahler metric is called central if the determinant of its Ricci endomorphism is constant. For the case in which this constant is zero, we study on $4$-manifolds the existence of complete metrics of this type which are cohomogeneity one…
A class of the $D=4$ gravity models describing a coupled system of $n$ Abelian vector fields and the symmetric $n \times n$ matrix generalizations of the dilaton and Kalb-Ramond fields is considered. It is shown that the Pecci-Quinn axion…
The finiteness condition of renormalization gives a restriction on the form of the gravitational action. By reconsidering the Hathrell's RG equations for massless QED in curved space, we determine the gravitational counterterms and the…
Properties of the two dimensional Ising model with fixed magnetization are deduced from known exact results on the two dimensional Ising model. The existence of a continuous phase transition is shown for arbitrary values of the fixed…
We investigate two-dimensional frustrated Heisenberg magnets using non-perturbative renormalization group techniques. These magnets allow for point-like topological defects which are believed to unbind and drive either a crossover or a…
Recent theoretical and experimental papers have shown how one can achieve Heisenberg limited measurements by using entangled photons. Here we show how the photons in non-collinear down conversion process can be used for improving the…
We identify the kinks of a deformed O(3) linear Sigma model as the solutions of a set of first-order systems of equations; the above model is a generalization of the MSTB model with a three-component scalar field. Taking into account…
Recent discovery of several van der waals magnetic material and moire magnet introduce to us an extremely challenging and revolutionary era of 2D magnetism and correlated phenomena for low dimensional material.More often the simplest spin…
Aharony and Fisher showed that non-local dipolar effects in magnetism destabilize the Heisenberg fixed point in real ferromagnets, leading to a new fixed point, called the dipolar fixed point. The non-perturbative nature of the new fixed…
We provide evidence for the existence of non-trivial unitary conformal boundary conditions for a three-dimensional free scalar field, which can be obtained via a coupling to the m'th unitary diagonal minimal model. For large m we can…
We consider a scalar field with a Gauss-Bonnet-type coupling to the curvature in a curved space-time. For such a quadratic coupling to the curvature, the metric energy-momentum tensor does not contain derivatives of the metric of orders…
Configurations of points defined by complex reflection groups have attracted a lot of attention recently in several directions of research, e.g., the containment problem between ordinary and symbolic powers of ideals, in the theory of…
Certain aspects of nonrelativistic diffeomorphisms in 2+1 dimensions are investigated. These include a nonrelativistic limit of some relativistic actions in 3 dimensions, the Seiberg-Witten map, a modification of the viscosity tensor in…
We discuss the Heisenberg model and its chiral extension in an extended truncation with the help of functional methods. Employing computer algebra to derive the beta functions, and pseudo-spectral methods to solve them, we are able to go…
We formulate the conformal bootstrap approach to four--fermion theory at its strong coupling fixed point in dimensions $2<d<4$. We present a solution of the bootstrap equations in the five--vertex approximation. We show that the bootstrap…
Let $H := \begin{pmatrix} 1 & {\mathbf R} & {\mathbf R} \\ 0 & 1 &{\mathbf R} \\ 0 & 0 & 1 \end{pmatrix}$ denote the Heisenberg group with the usual Carnot-Carath\'eodory metric $d$. It is known (since the work of Pansu and Semmes) that the…
The classical Heisenberg model has been solved in spatial d dimensins, exactly in d=1 and by the Migdal-Kadanoff approximation in d>1, by using a Fourier-Legendre expansion. The phase transition temperatures, the energy densities, and the…
Based on the quaternionic approach developed by one of us [Z.D. Zhang, Phil. Mag. 87 (2007) 5309.] for the three-dimensional (3D) Ising model, we study in this work conformal invariance in three dimensions. We develop a procedure for…
We investigate the static critical behaviour of a uniaxial magnetic layer, with finite thickness L in one direction, yet infinitely extended in the remaining d dimensions. The magnetic dipole-dipole interaction is taken into account. We…