Related papers: Stability of 3D Cubic Fixed Point in Two-Coupling-…
In this paper, we study the generalized Hyers-Ulam stability of Euler-Lagrange type cubic functional equation of the form \begin{align*} 2mf(x + my) + 2f(mx - y) = (m^3 + m)[f(x+ y) + f(x - y)] + 2(m^4 - 1)f(y) \end{align*} for all $x,y \in…
In cubic metals, a local, magnetic moment with a triplet ground state coupled to $\Gamma_8$ conduction electrons can give rise to various non-Fermi liquid (NFL) quantum critical behaviors. To date, only those exchange couplings have been…
The critical thermodynamics of an $MN$-component field model with cubic anisotropy relevant to the phase transitions in certain crystals with complicated ordering is studied within the four-loop $\ve$ expansion using the minimal subtraction…
We study models with three coupled vector fields characterized by $O(N_1)\oplus O(N_2) \oplus O(N_3)$ symmetry. Using the nonperturbative functional renormalization group, we derive $\beta$ functions for the couplings and anomalous…
We study the effect of the long-range Coulomb interaction in $j=3/2$ Dirac electrons in cubic crystals with the $O_h$ symmetry, which serves as an effective model for antiperovskite topological crystalline insulators. The renormalization…
The relative stability of three-dimensional icosahedral quasicrystals in multi-component systems has been investigated based on a coupled-mode Swift-Hohenberg model with two-length-scales. A recently developed projection method, which…
We are concerned with the stability of formation of large bipolaron in a 3-dimensional (3D) crystal. This problem is considered in the framework of nonrelativistic quantum field theory. Thus, the Hamiltonian formalism, as Froehlich…
Pad\'e-improvement of four-loop beta-functions in massive phi^4 scalar field theory is shown to predict the known five-loop contribution with astonishing (0.2%) accuracy, supporting the applicability of Pade-summations for approximating…
The stability of a quantum critical point in the $O(N)$ universality class with respect to an elastic coupling, that preserves $O(N)$ symmetry, is investigated for isotropic elasticity in the framework of the renormalization group (RG)…
We establish the Hatsugai-Kohmoto model as a stable quartic fixed point (distinct from Wilson-Fisher) by computing the $\beta-$function in the presence of perturbing local interactions. In vicinity of the half-filled doped Mott state, the…
A real space renormalization group technique, based on the hierarchical baby-universe structure of a typical dynamically triangulated manifold, is used to study scaling properties of 2d and 4d lattice quantum gravity. In 4d, the…
We revisit the equilibrium one-dimensional $\phi^4$ model from the dynamical systems point of view. We find an infinite number of periodic orbits which are computationally stable. At the same time some of the orbits are found to exhibit…
We consider the emergence of a non-Fermi liquid fixed point in a two-dimensional metal, at the onset of a quantum phase transition from a Fermi liquid state to an incommensurate charge density wave (CDW) ordered phase. The momentum of the…
We find novel perturbative fixed points by introducing mildly spacetime-dependent couplings into otherwise marginal terms. In four-dimensional QFT, these are physical analogues of the small-$\epsilon$ Wilson-Fisher fixed point. Rather than…
We study the $O(N)$-invariant $\phi^4$ model on the simple cubic lattice by using Monte Carlo simulations. By using a finite size scaling analysis, we obtain accurate estimates for the critical exponents $\nu$ and $\eta$ for $N=4$, $5$,…
We present a further study of the dynamics of high-dimension fermion operators attributed to the theoretical inconsistency of the fundamental cutoff (quantum gravity) and the parity-violating gauge symmetry of the standard model. Studying…
We consider the damped hyperbolic equation in one space dimension $\epsilon u_{tt} + u_t = u_{xx} + F(u)$, where $\epsilon$ is a positive, not necessarily small parameter. We assume that $F(0)=F(1)=0$ and that $F$ is concave on the interval…
We study the simplest quantum lattice spin model for the two-dimensional (2D) cubic ferromagnet by means of mean-field analysis and tensor network calculation. While both methods give rise to similar results in detecting related phases, the…
We consider the $O(N)^3$ tensor model of Klebanov and Tarnopolsky \cite{Klebanov:2016xxf} in $d<4$ with a free covariance modified to fit the infrared conformal scaling. We study the renormalization group flow of the model using a Wilsonian…
We formulate a renormalizable quantum gravity in $2+\epsilon$ dimensions by generalizing the nonlinear sigma model approach to string theory. We find that the theory possesses the ultraviolet stable fixed point if the central charge of the…