Related papers: Critical O(N) models above four dimensions: Small-…
Fixed-point equations in the functional renormalization group approach are integrated from large to vanishing field, where an asymptotic potential in the limit of large field is implemented as initial conditions. This approach allows us to…
We study the critical bosonic O(N) vector model with quenched random mass disorder in the large N limit. Due to the replicated action which is sometimes not bounded from below, we avoid the replica trick and adopt a traditional approach to…
We revisit the scalar $O(N)$ model in the dimension range $4<d<6$ and study the effects caused by its metastability. As shown in previous work, this model formally possesses a fixed point where, perturbatively in the $1/N$ expansion, the…
Whether O(N)-invariant conformal field theory exists in five dimensions with its implication to higher-spin holography was much debated. We find an affirmative result on this question by utilizing conformal bootstrap approach. In solving…
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…
We study the critical behavior of the $O(n)$ model under steady shear flow using a dynamical renormalization group (RG) method. Incorporating the strong anisotropy in scaling ansatz, which has been neglected in earlier RG analyses, we…
Classifying perturbative fixed points near upper critical dimensions plays an important role in understanding the space of conformal field theories and critical phases of matter. In this work, we consider perturbative fixed points of $N=5$…
We study fixed-points of scalar fields that transform in the bifundamental representation of $O(N)\times O(M)$ in $3-\epsilon$ dimensions, generalizing the classic tricritical sextic vector model. In the limit where $N$ is large but $M$ is…
We study the three dimensional O(N) invariant bosonic vector model with a $\frac{\lambda}{N}(\phi^{a}\phi^{a})^{2}$ interaction at its infrared fixed point, using a bilocal field approach and in an $1/N$ expansion. We identify a (negative…
Motivated by the prospect of quantum simulation of quantum field theories, we formulate the $O(N)$ nonlinear sigma model as a "qubit" model with an $(N+1)$-dimensional local Hilbert space at each lattice site. Using an efficient worm…
The effectiveness of the perturbative renormalization group approach at fixed space dimension d in the theory of critical phenomena is analyzed. Three models are considered: the O(N) model, the cubic model and the antiferromagnetic model…
We investigate the controversial issue of the existence of universality classes describing critical phenomena in three-dimensional statistical systems characterized by a matrix order parameter with symmetry O(2)xO(N) and symmetry-breaking…
The availability of scaling solutions in renormalisation group improved versions of cosmology are investigated in the high-energy limit. We adopt $f(R)$-type models of quantum gravity which display an interacting ultraviolet fixed point at…
Logarithmic finite-size scaling of the O($n$) universality class at the upper critical dimensionality ($d_c=4$) has a fundamental role in statistical and condensed-matter physics and important applications in various experimental systems.…
It is shown that the infinite dimensional critical surface of general euclidean lattice actions in a generic four-dimensional scalar field theory with $\Phi^4$ interactions has a domain of special multicritical points where higher…
We review the theoretical description of the random field Ising and $O(N)$ models obtained from the functional renormalization group, either in its nonperturbative implementation or, in some limits, in perturbative implementations. The…
We employ the axiomatic framework of Rychkov and Tan to investigate the critical O$(N)$ vector model with a line defect in $(4-\epsilon)$ dimensions. We assume the fixed point is described by defect conformal field theory and show that the…
We study O(N) models with power-law interactions by using functional renormalization group methods: we show that both in Local Potential Approximation (LPA) and in LPA' their critical exponents can be computed from the ones of the…
We consider the zero-dimensional O(N) vector model as a simple example to calculate n-point correlation functions using perturbation theory, the large-N expansion, and the functional renormalization group (FRG). Comparing our findings with…
Random tensor models can be used as combinatorial devices to generate Euclidean dynamical triangulations. A physical continuum limit of dynamical triangulations requires a suitable generalization of the double-scaling limit of random…