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We consider the Ginzburg-Landau Hamiltonian with a cubic-symmetric quartic interaction and compute the renormalization-group functions to six-loop order in d=3. We analyze the stability of the fixed points using a Borel transformation and a…
We study the cubic fixed point for $N=3$ and $4$ by using finite size scaling applied to data obtained from Monte Carlo simulations of the $N$-component $\phi^4$ model on the simple cubic lattice. We generalize the idea of improved models…
A tensorial representation of $\phi^4$ field theory introduced in Phys. Rev. D. 93, 085005 (2016) is studied close to six dimensions, with an eye towards a possible realization of an interacting conformal field theory in five dimensions. We…
We compute renormalization group fixed points and their spectrum in an ultralocal approximation. We study a case of two competing non-trivial fixed points for a three-dimensional real $N$-component field: the O(N)-invariant fixed point…
We study the stability of the O(N) fixed point in three dimensions under perturbations of the cubic type. We address this problem in the three cases $N=2,3,4$ by using finite size scaling techniques and high precision Monte Carlo…
For the anisotropic $[u (\sum_{i=1^N {\phi}_i^2)^2+v \sum_{i=1^N \phi_i^4]$-theory with {$N=2,3$} we calculate the imaginary parts of the renormalization-group functions in the form of a series expansion in $v$, i.e., around the isotropic…
Within the four-loop $\ve$ expansion, we study the critical behavior of certain antiferromagnets with complicated ordering. We show that an anisotropic stable fixed point governs the phase transitions with new critical exponents. This is…
In search of non-trivial field theories in high dimensions, we study further the tensor representation of the $O(N)$-symmetric $\phi^4$ field theory introduced by Herbut and Janssen (Phys. Rev. D. 93, 085005 (2016)), by using four-loop…
We study the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy. We compute and analyze the fixed-dimension perturbative expansion of the renormalization-group functions to four loops. The relations of these…
Critical fluctuations are known to change the effective anisotropy of cubic ferromagnet near the Curie point. If the crystal undergoes phase transition into orthorhombic phase and the initial anisotropy is not too strong, effective…
We consider $\phi^3$ theory in $6-2\epsilon$ with $F_4$ global symmetry. The beta function is calculated up to 3 loops, and a stable unitary IR fixed point is observed. The anomalous dimensions of operators quadratic or cubic in $\phi$ are…
Critical fluctuations change the effective anisotropy of cubic ferromagnet near the Curie point. If the crystal undergoes phase transition into orthorhombic phase and the initial anisotropy is not too strong, reduced anisotropy of nonlinear…
We study the scalar $\phi^3$ theory above six dimensions. The beta function $\beta(g)=-\epsilon g-\frac{3}{4}g^3$ in $d=6-2\epsilon$ dimensions has a UV fixed point when $\epsilon<0$. Like the $O(N)$ vector models above four dimensions,…
We consider $O(N)$-symmetric bosonic $\phi^4$ field theories above four dimensions, and propose a new reformulation in terms of an irreducible tensorial field with a cubic and Yukawa terms. The $\phi^4$ field theory so rewritten exhibits…
We study the stability of the critical points of the Onsager energy functional with Maier-Saupe interaction potential in general dimensions. We show that the stable critical points must be axisymmetric, which solves a problem proposed by…
We study the stability of fixed points in the two-loop renormalization group for the random field O($N$) spin model in $4+\epsilon$ dimensions. We solve the fixed-point equation in the 1/N expansion and $\epsilon$ expansion. In the large-N…
It was shown recently that a PT-symmetric $i\phi^3$ quantum field theory in $6-\epsilon$ dimensions possesses a nontrivial fixed point. The critical behavior of this theory around the fixed point is examined and it is shown that the…
The Euclidean $(\phi^{4})_{3,\epsilon$ model in $R^3$ corresponds to a perturbation by a $\phi^4$ interaction of a Gaussian measure on scalar fields with a covariance depending on a real parameter $\epsilon$ in the range $0\le \epsilon \le…
We study large charge sectors in the $O(N)$ model in $6-\epsilon $ dimensions. For $4<d<6$, in perturbation theory, the quartic $O(N)$ theory has a UV stable fixed point at large $N$. It was recently argued that this fixed point can be…
We study the critical behavior of a general class of cubic-symmetric spin systems in which disorder preserves the reflection symmetry $s_a\to -s_a$, $s_b\to s_b$ for $b\not= a$. This includes spin models in the presence of random…