Related papers: Farey Tree and the Frenkel-Kontorova Model
A discrete Frenkel-Kontorova model with two alternate spring constants $k_{1}$ and $k_{2}$ is studied. It is found that this model has many surprising behaviours. The continuum version of this model is different from the sine-Gordon…
In this paper, we have studied the one-dimensional commensurate quantum Frenkel-Kontorova model by a density-matrix renormalization group (DMRG) algorithm. The focus has been on its properties of the entanglement, the coordinate…
The ground state configurations of the one--dimensional Falicov--Kimball model are studied exactly with numerical calculations revealing unexpected effects for small interaction strength. In neutral systems we observe molecular formation,…
We propose the Landau model for lock-in phase transitions in uniaxially modulated improper ferroelectric incommensurate-commensurate systems of class I. It includes Umklapp terms of third and fourth order and secondary order parameter…
In this paper, it is shown that a configuration modulated system described by the Frenkel-Kontorova model can be locked at an incommensurate phase when the quantum zero point energy is taken into account. It is also found that the specific…
We apply the theory of markov random fields on trees to derive a phase transition in the number of samples needed in order to reconstruct phylogenies. We consider the Cavender-Farris-Neyman model of evolution on trees, where all the inner…
We calculate the $\theta$ dependence in a cousin of QCD, where the vacuum structure can be analyzed exactly. The theory is $\mathcal{N}=2$ $SU(2)$ gauge theory with $N_F=0,1,2,3$ flavors of fundamentals, explicitly broken to $\mathcal{N}=1$…
One may argue that QCD solves the strong CP problem by itself, without having to introduce new symmetries and particles. To test this idea, a lattice simulation is performed. The problem is investigated in the CP$^3$ model first. It is…
A procedure is described for efficiently finding the ground state energy and configuration for a Frenkel-Kontorova model in a periodic potential, consisting of N parabolic segments of identical curvature in each period, through a numerical…
We discuss a model for phase transitions in which a double-well potential is singularly perturbed by possibly several terms involving different, arbitrarily high orders of derivation. We study by $\Gamma$-convergence the asymptotic…
In this paper we complete the analysis of a statistical mechanics model on Cayley trees of any degree, started in [EsHaRo12,EsRo10,BoEsRo13,JaKuBo14,Bo17]. The potential is of nearest-neighbor type and the local state space is compact but…
Assuming triviality of the 4-dimensional $\lambda \phi ^4$-theory we compute the effective potential by means of a self consistent Feynman-Bogoliubov method. This potential $U_{eff}^{FB}$ depends on a UV-cutoff, which is fixed by a…
In this paper, the one-dimensional incommensurate quantum Frenkel-Kontorova model is investigate by a density-matrix renormalization group algorithm. Special attention is given to the entanglement and the ground state energy. The energy gap…
The nonlinear response of an adsorbed layer on a periodic substrate to an external force is studied via a two dimensional uniaxial Frenkel-Kontorova model. The nonequlibrium properties of the model are simulated by Brownian molecular…
Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and…
We study the Electroweak phase transition with the Standard Model effective field theory at finite temperature and finite density. Utilizing the dimensional reduction approach, we construct the tree dimensional thermal effective field…
The global center symmetry of quenched QCD at zero baryonic chemical potential is broken spontaneously at a critical temperature $T_c$ leading to a first-order phase transition. Including heavy dynamical quarks breaks the center symmetry…
We consider the random wetting transition on the Cayley tree, i.e. the problem of a directed polymer on the Cayley tree in the presence of random energies along the left-most bonds. In the pure case, there exists a first-order transition…
The ground states of the one-dimensional Falicov-Kimball model are investigated in the small-coupling limit, using nearly degenerate perturbation theory. For rational electron and ion densities, respectively equal to $\frac{p}{q}$,…
We study analytically and numerically the one-dimensional quantum Frenkel-Kontorova chain in the regime when the classical model is located in the pinned phase characterized by the gaped phonon excitations and devil's staircase. By…