Related papers: A plane defect in the 3d O$(N)$ model
We study the critical properties of scalar field theories in $d+1$ dimensions with $O(N)$ invariant interactions localized on a $d$-dimensional boundary. By a combination of large $N$ and epsilon expansions, we provide evidence for the…
We show with two numerical examples that the conventional expansion in powers of the field for the critical potential of 3-dimensional O(N) models in the large-N limit, does not converge for values of phi^2 larger than some critical value.…
Let $\Omega$ be a bounded domain in $\mathbb R^{N}$, $N\geq3$ with smooth boundary, $a>0, \lambda>0$ and $0<\delta<3$ be real numbers. Define $2^*:=\displaystyle\frac{2N}{N-2}$ and the characteristic function of a set $A$ by $\chi_A$. We…
The renormalized trajectory in the multi-dimensional coupling parameter space of the two-dimensional O(3) non-linear sigma model is determined numerically under \linebreak $\delta$-function block spin transformations using two different…
The Erd\H{o}s distinct distance problem is a ubiquitous problem in discrete geometry. Less well known is Erd\H{o}s' distinct angle problem, the problem of finding the minimum number of distinct angles between $n$ non-collinear points in the…
The resurgence structure of the 2d $O(N)$ sigma model at large $N$ is studied with a focus on an IR momentum cutoff scale $a$ that regularizes IR singularities in the semiclassical expansion. Transseries expressions for condensates and…
We consider a general class of two-dimensional spin systems, with continuous but not necessarily smooth, possibly long-range, $O(N)$-symmetric interactions, for which we establish algebraically decaying upper bounds on spin-spin…
We investigate the critical properties of the three-dimensional (3D) antiferromagnetic RP(N-1}) model, which is characterized by a global O(N) symmetry and a discrete Z_2 gauge symmetry. We perform a field-theoretical analysis using the…
Numerical solutions of Einstein's and scalar-field equations are found for a global defect in a higher-dimensional spacetime. The defect has a $(3+1)$-dimensional core and a ``hedgehog'' scalar-field configuration in $n=3$ extra dimensions.…
The critical behaviour of the O(n)-symmetric model with two n-vector fields is studied within the field-theoretical renormalization group approach in a D=4-2 epsilon expansion. Depending on the coupling constants the beta-functions, fixed…
We study how universality classes of O(N)-symmetric models depend continuously on the dimension d and the number of field components N. We observe, from a renormalization group perspective, how the implications of the…
We use the functional renormalization group and the $\epsilon$-expansion concertedly to explore multicritical universality classes for coupled $\bigoplus_i O(N_i)$ vector-field models in three Euclidean dimensions. Exploiting the…
Boundary conformal field theory (BCFT) provides a universal framework for critical phenomena in the presence of boundaries. We determine BCFT data for the normal and ordinary boundary universality classes of the $1+1$-dimensional boundaries…
The classical no-three-in-line problem asks for the largest number (D(n)) of points that can be chosen from an (n \times n) grid with no three collinear. We study the checkerboard-restricted variant in which all chosen points lie in one…
We study symmetry-breaking line defects in the Wilson-Fisher theory with $O(2N+1)$ global symmetry near four dimensions and symmetry-preserving surface defects in a cubic model with $O(2N)$ global symmetry near six dimensions. We introduce…
We investigate a two-dimensional statistical model of N charged particles interacting via logarithmic repulsion in the presence of an oppositely charged compact region K whose charge density is determined by its equilibrium potential at an…
We show that a generic real projective $n$-dimensional hypersurface of odd degree $d$, such that $4(n-2)=\binom{d+3}3$, contains "many" real 3-planes, namely, in the logarithmic scale their number has the same rate of growth, $d^3\log d$,…
Let $\Omega\subset\mathbb R^2$ be a chord arc domain. We give a simple proof of the the following fact, which is commonly known to be true: a nontrivial harmonic function which vanishes continuously on a relatively open set of the boundary…
We find that the multicritical fixed point structure of the O($N$) models is much more complicated than widely believed. In particular, we find new nonperturbative fixed points in three dimensions ($d=3$) as well as at $N=\infty$. These…
We argue that the two-dimensional $O(N)$-invariant lattice $\sigma$-model with mixed isovector/isotensor action has a one-parameter family of nontrivial continuum limits, only one of which is the continuum $\sigma$-model constructed by…