Two and Three-Dimensional Spin Systems with Gonihedric Action

We perform numerical simulations of the two and three-dimensional spin systems with competing interaction. They describe the model of random surfaces with linear-gonihedric action.The degeneracy of the vacuum state of this spin system is equal to $~~d \cdot 2^{N}~~$ for the lattice of the size $~N^{d}~$. We observe the second order phase transition of the three-dimensional system, at temperature $\beta_{c} \simeq 0.43932$ which almost coincides with $\beta_{c}$ of the 2D Ising model. This confirms the earlier analytical result for the case when self-interaction coupling constant $k$ is equal to zero. We suggest the full set of order parameters which characterize the structure of the vacuum states and of the phase transition.Comment: 10 pages,Latex,The figures are availabl

Evidence for a first order transition in a plaquette 3d Ising-like action

We investigate a 3d Ising action which corresponds to a a class of models defined by Savvidy and Wegner, originally intended as discrete versions of string theories on cubic lattices. These models have vanishing bare surface tension and the couplings are tuned in such a way that the action depends only on the angles of the discrete surface, i.e. on the way the surface is embedded in ${\bf Z}^3$. Hence the name gonihedric by which they are known. We show that the model displays a rather clear first order phase transition in the limit where self-avoidance is neglected and the action becomes a plaquette one. This transition persists for small values of the self avoidance coupling, but it turns to second order when this latter parameter is further increased. These results exclude the use of this type of action as models of gonihedric random surfaces, at least in the limit where self avoidance is neglected.Comment: 4 pages Latex text, 4 postscript figure

String tension in gonihedric 3D Ising models

For the 3D gonihedric Ising models defined by Savvidy and Wegner the bare string tension is zero and the energy of a spin interface depends only on the number of bends and self-intersections, in antithesis to the standard nearest-neighbour 3D Ising action. When the parameter kappa weighting the self-intersections is small the model has a first order transition and when it is larger the transition is continuous. In this paper we investigate the scaling of the renormalized string tension, which is entirely generated by fluctuations, using Monte Carlo simulations This allows us to obtain an estimate for the critical exponents alpha and nu using both finite-size-scaling and data collapse for the scaling function.Comment: Latex + postscript figures. 8 pages text plus 7 figures, spurious extra figure now removed

The ππ\pi \pi S-Wave in the 1 to 2 GeV Region from a ππ\pi \pi, KˉK\bar{K}K and ρρ\rho \rho(ωω\omega \omega) Coupled Channel Model

A simple $\pi \pi$, $\bar{K}K$, and $\rho \rho$($\omega \omega$) fully coupled channel model is proposed to predict the isoscalar S-wave phase shifts and inelasticities for $\pi \pi$ scattering in the 1.0 to 2.0 GeV region. The S-matrix is required to exhibit poles corresponding to the established isoscalar J$^{\pi}$ = 0$^+$ resonances f$_0$(975), f$_0$(1400), and f$_0$(1710). A dominant feature of the experimental $\pi \pi$ inelasticity is the clear opening of the $\bar{K}K$ channel near 1 GeV, and the opening of another channel in the 1.4 - 1.5 GeV region. The success of our model in predicting this observed dramatic energy dependence indicates that the effect of multi-pion channels is adequately described by the $\pi \pi$ coupling to the $\bar{K}K$ channel, the $\rho \rho$(4$\pi$) and $\omega \omega$(6$\pi$) channels.Comment: 11 pages (Revtex 3.0), 4 figs. avail. upon request, RU946

Three-dimensional Gonihedric Potts model

We study, by the Mean Field and Monte Carlo methods, a generalized q-state Potts gonihedric model. The phase transition of the model becomes stronger with increasing $q.$ The value $k_c(q),$ at which the phase transition becomes second order, turns out to be an increasing function of $q.$Comment: 11 pages, 7 figure

Slow dynamics in the 3--D gonihedric model

We study dynamical aspects of three--dimensional gonihedric spins by using Monte--Carlo methods. The interest of this family of models (parametrized by one self-avoidance parameter $\kappa$) lies in their capability to show remarkably slow dynamics and seemingly glassy behaviour below a certain temperature $T_g$ without the need of introducing disorder of any kind. We consider first a hamiltonian that takes into account only a four--spin term ($\kappa=0$), where a first order phase transition is well established. By studying the relaxation properties at low temperatures we confirm that the model exhibits two distinct regimes. For $T_g< T < T_c$, with long lived metastability and a supercooled phase, the approach to equilibrium is well described by a stretched exponential. For $T<T_g$ the dynamics appears to be logarithmic. We provide an accurate determination of $T_g$. We also determine the evolution of particularly long lived configurations. Next, we consider the case $\kappa=1$, where the plaquette term is absent and the gonihedric action consists in a ferromagnetic Ising with fine-tuned next-to-nearest neighbour interactions. This model exhibits a second order phase transition. The consideration of the relaxation time for configurations in the cold phase reveals the presence of slow dynamics and glassy behaviour for any $T< T_c$. Type II aging features are exhibited by this model.Comment: 13 pages, 12 figure

Annihilation range and final-state interaction in the antiproton-proton annihilation into pi-pi+

The large set of accurate data on differential cross section and analyzing power from the CERN LEAR experiment on $\bar pp \to \pi^+\pi^-$ in the range from 360 to 1550 MeV/c is well reproduced within a distorted wave approximation approach. The initial $\bar pp$ scattering wave functions originate from a recent $\bar N N$ model. The transition operator is obtained from a combination of the $^3P_0$ and $^3S_1$ quark-antiquark annihilation mechanisms. A good fit to the data, in particular the reproduction of the double dip structure observed in the analyzing powers, requires quark wave functions for proton, antiproton, and pions with radii slightly larger than the respective measured charge radii. This corresponds to an increase in range of the annihilation mechanisms and consequently the amplitudes for total angular momentum J=2 and higher are much larger than in previous approaches. The final state $\pi\pi$ wave functions, parameterized in terms of $\pi\pi$ phase shifts and inelasticities, are also a very important ingredient for the fine tuning of the fit to the observables.Comment: 11 pages, 11 figures (Revtex 4), revised version with one additional figure. Accepted for publication in PR

An amplitude analysis of the N‾N→π−π+\overline{N}N \to \pi^- \pi^+ reaction

A simple partial wave amplitude analysis of $\overline{p}p \rightarrow \pi^- \pi^+$ has been performed for data in the range p_{\sl lab} = 360 -- 1000 MeV/c. Remarkably few partial waves are required to fit the data, while the number of required $J$ values barely changes over this energy range. However, the resulting set of partial wave amplitudes is not unique. We discuss possible measurements with polarized beam and target which will severely restrict and help resolve the present analysis ambiguities. New data from the reaction $\overline{p}p \rightarrow \pi^0 \pi^0$ alone, are insufficient for that purpose.Comment: 16 pages (revtex), 8 figures available on request, submitted to Phys. Rev.