Related papers: Marginal dimensions for multicritical phase transi…
We look at the influence of external fields on systems described by generic free energy functional of the order parameter. The external force may have arbitrary spatial dependence, and the order parameter coupling may be nonlinear. The…
The mean-field optical phase transition in multimode equal-coupling photonic networks is studied by temporal evolution of the nonlinear equations of motion of the coupled modes. Analogies to statistical mechanics models of interacting…
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…
The phase diagram of a system with two order parameters, with ${\it n_1}$ and $n_2$ components, respectively, contains two phases, in which these order parameters are non-zero. Experimentally and numerically, these phases are often…
A non-perturbative Renormalization Group approach is used to calculate scaling functions for an O(4) model in d=3 dimensions in the presence of an external symmetry-breaking field. These scaling functions are important for the analysis of…
We study the surface scaling behavior of a semi-infinite $d$-dimensional O(N) spin system in the presence of quenched random field and random anisotropy disorders. It is known that above the lower critical dimension $d_{\mathrm{lc}}=4$ the…
The critical behavior of $d$-dimensional systems with $n$-component order parameter $\bm{\phi}$ is studied at an $m$-axial Lifshitz point where a wave-vector instability occurs in an $m$-dimensional subspace ${\mathbb R}^m$ ($m{>}1$). Field…
We propose a new criterion to analyse the order of phase transitions within a finite size scaling analysis. It refers to response functions like order parameter susceptibilities and the specific heat and states different monotony behaviour…
Critical behaviour of the O(n)-symmetric $\phi^{4}$-model with an antisymmetric tensor order parameter is studied by means of the field-theoretic renormalization group (RG) in the leading order of the $\varepsilon=4-d$-expansion (one-loop…
The critical behavior of a model with N-vector complex order parameter and three quartic coupling constants that describes phase transitions in unconventional superconductors, helical magnets, stacked triangular antiferromagnets, superfluid…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…
The global phase diagrams of the Askin-Teller model are calculated in d=2 and 3 by renormalization-group theory that is exact on the hierarchical lattice and approximate on the recently improved Migdal-Kadanoff procedure. Three different…
We use nematic Multi-particle Collision Dynamics (N-MPCD) simulations to study confined nematic liquid crystals in square domains, with three distinct mean-field potentials: the classical Maier-Saupe and Marrucci-Greco models, and a more…
Two-dimensional materials with interacting Dirac excitations can host quantum multicritical behavior near the phase boundaries of the semimetallic and two-ordered phases. We study such behavior in Gross--Neveu--Yukawa field theories where…
We study the multicritical behavior arising from the competition of two distinct types of ordering characterized by O(n) symmetries. For this purpose, we consider the renormalization-group flow for the most general $O(n_1)\oplus…
The Landau-Wilson field theory with $O(n)\times O(m)$ symmetry which describes the critical thermodynamics of frustrated spin systems with noncollinear and noncoplanar ordering is analyzed in $4 - \varepsilon$ dimensions within the minimal…
A biologically motivated model for spatio-temporal coexistence of two competing species is studied by mean-field theory and numerical simulations. In d>1 dimensions the phase diagram displays an extended region where both species coexist,…
An introduction into the theory of boundary critical phenomena and the application of the field-theoretical renormalization group method to these is given. The emphasis is on a discussion of surface critical behavior at bulk critical points…
The critical behaviour of $d$-dimensional semi-infinite systems with $n$-component order parameter $\bm{\phi}$ is studied at an $m$-axial bulk Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional subspace of…
We investigate the phase structure of non-commutative scalar field theories and find evidence for ordered phases which break translation invariance. A self-consistent one-loop analysis indicates that the transition into these ordered phases…