Related papers: Renormalization of Fluctuating Tilted-Hexatic Memb…
The phase diagram for the interacting fermions in weak coupling is described by the perturbative renormalization group equations. Due to the lack of analytic solutions for these coupled non-linear differential equations, it is rather subtle…
We review recent computer simulation studies of undulating lipid bilayers. Theoretical interpretations of such fluctuating membranes are most commonly based on generalized Helfrich-type elastic models, with additional contributions of local…
We consider a system of dynamically-modulated photonic resonator lattice undergoing photonic transition, and show that in the ultra-strong coupling regime such a lattice can exhibit non-trivial topological properties, including…
We analyse the effect of thermal fluctuations on the elastic constants of the decoupled lamellar phase of tethered, crystalline membranes. Using a momentum-shell renormalization group technique, we show that the smectic-A -like…
We point out that the smectic-nematic phase transition may considered as a transition of a stack of membranes in $2+\epsilon$ dimensions, in which the layers become so wrinkled that they interpenetrate each other are no longer…
The theory of thermal fluctuations in crystalline membranes is put under scrutiny. In particular, the two critical regimes of the renormalisation group diagram, which are often left out of the discussion because of their instability in one…
We present the phase diagram and critical properties of a coupled $XY$-Ising model on a triangular lattice using the mean-field approximation, the Migdal-Kadanoff scheme of renormalization group and Monte-Carlo simulations. The topology of…
We study the behavior of the renormalized sextic coupling at the intermediate and strong coupling regime for the $\phi^4 $ theory defined in $d=2$-dimension. We found a good agreement with the results obtained by the field-theoretical…
The sliding columnar phase is a new liquid-crystalline phase of matter composed of two-dimensional smectic lattices stacked one on top of the other. This phase is characterized by strong orientational but weak positional correlations…
One investigates the flat phase of quenched disordered polymerized membranes by means of a two-loop, weak-coupling computation performed near their upper critical dimension $D_{uc} = 4$, generalizing the one-loop computation of Morse,…
Normal--mode splitting is the most evident signature of strong coupling between two interacting subsystems. It occurs when two subsystems exchange energy between themselves faster than they dissipate it to the environment. Here we…
We investigate the Kosterlitz-Thouless transition for hexatic order on a free fluctuating membrane and derive both a Coulomb gas and a sine-Gordon Hamiltonian to describe it. The Coulomb-gas Hamiltonian includes charge densities arising…
The vulcanization transition - the crosslink-density-controlled equilibrium phase transition from the liquid to the amorphous solid state - is explored analytically from a renormalization group perspective. The analysis centers on a minimal…
We study the weak coupling limit of the Anderson Hamiltonian in the critical dimension $d=4$. In a perturbative sense, we prove Gaussian fluctuations about the Green's function of the Laplacian. The fluctuations are described by an explicit…
Understanding overcharging and charge inversion is one of the long-standing challenges in soft matter and biophysics. To study these phenomena, we employ the modified Gaussian renormalized fluctuation theory, which allows for the…
Based on exact diagonalization and density matrix renormalization group (DMRG) method, we show that an anisotropic triangle lattice Heisenberg spin model has three distinct quantum phases. In particular, a spin-liquid phase is present in…
We consider close-packed tiling models of geometric objects -- a mixture of hardcore dimers and plaquettes -- as a generalisation of the familiar dimer models. Specifically, on an anisotropic cubic lattice, we demand that each site be…
We investigate the renormalization group flows and fixed point structure of many coupled minimal models. The models are coupled two by two by energy-energy couplings. We take the general approach where the bare couplings are all taken to be…
We investigate the phase behaviour of a two-dimensional colloidal model system of ultra-soft particles on a substrate which varies periodically along one spatial direction. Our calculations are based on mean-field density functional theory…
We derive an efficient method for treating renormalization contributions at two-loop level within the functional renormalization group in the one-particle irreducible formalism for fermions. It is based on a decomposition of the…