Yukawa model on a lattice: Two-body states

We present some Quantum Field Theory (QFT) results concerning the Yukawa model, solved non-perturbatively with the help of lattice techniques. In particular we focus on the possibility of generating a two-nucleon bound state, as compared to the non-relativistic limit of the same model. Preliminary results show the appearance of zero modes of the Dirac operator. They limit the numerical solution of the model to values of the coupling constant which are too small to allow binding of the two-nucleon system.     

Mass of a lattice polaron from an extended Holstein model using the Yukawa potential

Renormalization of the mass of an electron is studied within the framework of the Extended Holstein model at strong coupling regime and nonadiabatic limit. In order to take into account an effect of screening of an electron-phonon interaction on a polaron it is assumed that the electron-phonon interaction potential has the Yukawa form and screening of the electron-phonon interaction is due to the presence of other electrons in a lattice. The forces are derived from the Yukawa type electron-phonon interaction potential. It is emphasized that the early considered screened force of (Kornilovitch (1998), Spencer et al. (2005), Hague et al. (2006), Hague and Kornilovitch (2009)) Refs. [7], [18], [19] and [22] is a particular case of the force deduced from the Yukawa potential and is approximately valid at large screening radiuses compared to the distances under consideration. The Extended Holstein polaron with the Yukawa type potential is found to be a more mobile than polaron studied in early works at the same screening regime.     

The nuclear lattice model of proton-induced multi-fragmentation reactions

A model of proton-induced multi-fragmentation reactions based on percolation theory is described and applied to experimental data. With only the simplest of assumptions the essential features of the mass-yield curves, such as their U-shape and their power-law dependence for low-to-medium masses, are reproduced. However, the model is, as will be demonstrated, flexible enough to allow for the inclusion of different physical mechanisms. The fits to mass-yield data are then quantitative over the whole mass range. The connection with real physics is made and some relevant experiments are suggested.     

The Skyrme model on a four-dimensional lattice

The SU(2) Skyrme model is formulated on a four-dimensional lattice with the nearest and next-to-nearest neighbor interactions in the action. To establish a continuum limit, the phase structure is studied and the order of phase transition is determined by various methods. Coexistence of two phases and hysteresis effect are observed at the critical point, indicating a first-order phase transition in the parameter space.     

The Skyrme model on a four-dimensional lattice

The SU(2) Skyrme model is formulated on a four-dimensional lattice with the nearest and next-to-nearest neighbor interactions in the action. To establish a continuum limit, the phase structure is studied and the order of phase transition is determined by various methods. Coexistence of two phases and hysteresis effect are observed at the critical point, indicating a first-order phase transition in the parameter space.     

Fermion masses in a strong Yukawa coupling model

For strong enough Yukawa coupling the electroweak standard model fermion finds it energetically advantageous to transform itself into a bound state in the hedgehog background of the Higgs field in the semiclassical approximation. By considering that the bound states give the masses for the lepton and quark, it is found that all fermion masses can be described by the strongly Yukawa coupling constants which tend to a unitary constant.     

Critical exponents for nuclear multifragmentation: dynamical lattice model

We present a dynamical and dissipative lattice model, designed to mimic nuclear multifragmentation. Monte Carlo simulations with this model show a clear signature of critical behaviour and reproduce experimentally observed correlations. In particular, using techniques devised for finite systems, we could obtain two of its critical exponents, whose values are in agreement with those of the universality class to which nuclear multifragmentation is supposed to belong.     

The bond bending model on triangular lattice and square lattice

The bond bending model is studied using the series expansion method on a triangular lattice and on a square lattice. The elastic splay susceptibility χ_SR and the elastic compressional susceptibility χ_el are calculated up to 11th order for the triangular lattice and up to 14th order for the square lattice. The elastic splay crossover exponent, ζ_SP, is found to be ζ_SP ≈ 1.26 ± 0.05 for the triangular lattice and ζ_SP = 1.30 ± 0.04 for the square lattice which is close to the conductivity exponent, ζ_Re, of the resistor network. From the scaling relation ? _B = dv + ζ_SP, we found that the bulk modulus exponent ? _B = 3.93 ± 0.05 for the triangular lattice and ? _B = 3.97 ± 0.04 for the square lattice which is in good agreement with the result ? _B = 3.96 ± 0.04, obtained by Zabolitzky et al. using a transfer matrix technique on a honeycomb lattice.     

The geometrical phase transitions in a lattice model

We shall consider a finite range model on a square latticeZ ³ and show the existence of bubble, tubular and lamellar phases by estimating the correlation functions at low temperature.     

Low dimensional ordering on a lattice model

A simple d-dimensional lattice model is proposed, incorporating some degree of frustration and thus capable of describing some aspects of molecular orientation in covalently bound molecular solids. For d = 2 the model is shown to be equivalent to the standard two-dimensional Ising model, while for d > 2 it describes a peculiar transition from an isotropic high temperature phase to a low-dimensional anisotropic low temperature state. A general mean field analysis is presented and compared to some exact limit properties.