Related papers: Isotropic Lifshitz Scaling in four dimensions
The Kosterlitz-Thouless phase transition is described by the nonperturbative renormalization flow of the two dimensional $\phi^4$-model. The observation of essential scaling demonstrates that the flow equation incorporates nonperturbative…
We investigate critical $N$-component scalar field theories and the spontaneous breaking of scale invariance in three dimensions using functional renormalisation. Global and local renormalisation group flows are solved analytically in the…
Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O(2) vector model characterised by non linear nearest neighbour spin interaction governed by the fourth Legendre polynomial $P\_4$. The…
We study O(n)-symmetric two-dimensional conformal field theories (CFTs) for a continuous range of n below two. These CFTs describe the fixed point behavior of self-avoiding loops. There is a pair of known fixed points connected by an RG…
The critical behavior of a non-local scalar field theory is studied. This theory has a non-local quartic interaction term which involves a real power -\beta of the Laplacian. The parameter \beta can be tuned so as to make that interaction…
The critical behaviour of d-dimensional n-vector models at m-axial Lifshitz points is considered for general values of m in the large-n limit. It is proven that the recently obtained large-N expansions [J. Phys.: Condens. Matter 17, S1947…
We explore universal critical behavior in models with two competing order parameters, and an O(N)+O(M) symmetry for dimensions $d \leq 3$. In d=3, there is always exactly one stable Renormalization Group fixed point, corresponding to…
We study the quantum criticality of the Lifshitz $\varphi^4$-theory below the upper critical dimension. Two fixed points, one Gaussian and the other non-Gaussian, are identified with zero and finite interaction strengths, respectively. At…
A new variant of the Wolff cluster algorithm is proposed for simulating systems with competing interactions. This method is used in a high-precision study of the Lifshitz point of the 3D ANNNI model. At the Lifshitz point, several critical…
We present analytical results for the finite-size scaling in d--dimensional O(N) systems with strong anisotropy where the critical exponents (e.g. \nu_{||} and \nu_{\perp}) depend on the direction. Prominent examples are systems with…
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…
We renormalize various scalar field theories with a $\phi^n$ self interaction such as $n$ $=$ $5$, $7$ and $9$ in their respective critical dimensions which are non-integer. The renormalization group functions for the $O(N)$ symmetric…
The puzzle of the disappearance of isotropic Lifshitz points in condensed matter physics is explained from the point of view of the Wilsonian renormalization group. In analogy to the commensurate ideas of metamagnetic phase transitions, we…
We prove the existence of macroscopic loops in the loop O(2) model with $\frac12\leq x^2\leq 1$ or, equivalently, delocalisation of the associated integer-valued Lipschitz function on the triangular lattice. This settles one side of the…
We study tree-unitarity and renormalizability in Lifshitz-scaling theory, which is characterized by an anisotropic scaling between the spacial and time directions. Due to the lack of the Lorentz symmetry, the conditions for both unitarity…
We demonstrate the existence of a universal transition from a continuous scale invariant phase to a discrete scale invariant phase for a class of one-dimensional quantum systems with anisotropic scaling symmetry between space and time.…
The two-dimensional ferromagnetic anisotropic Ashkin-Teller model is investigated through a real-space renormalization-group approach. The critical frontier, separating five distinct phases, recover all the known exacts results for the…
We investigate whether 4-dimensional static and cosmological Lifshitz solutions can be found from deforming the existing (A)dS_4 compactifications in IIA and IIA* supergravity. Using a well motivated compactification Ansatz on…
We review recent activity in the construction of the renormalization group functions for O(N) scalar and gauge theories in six and higher dimensions. The theories lie in their respective universality classes at the Wilson-Fisher fixed…
The extension of strongly anisotropic or dynamical scaling to local scale invariance is investigated. For the special case of an anisotropy or dynamical exponent $\theta=z=2$, the group of local scale transformation considered is the…