Loop transfer matrix and gonihedric loop diffusion

We study a class of statistical systems which simulate 3D gonihedric system on euclidean lattice. We have found the exact partition function of the 3D-model and the corresponding critical indices analysing the transfer matrix $K(P_{i},P_{f})$ which describes the propagation of loops on a lattice. The connection between 3D gonihedric system and 2D-Ising model is clearly seen.Comment: 14 pages, Late

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

GEOMETRICAL STRING and DUAL SPIN SYSTEMS

We are able to perform the duality transformation of the spin system which was found before as a lattice realization of the string with linear action. In four and higher dimensions this spin system can be described in terms of a two-plaquette gauge Hamiltonian. The duality transformation is constructed in geometrical and algebraic language. The dual Hamiltonian represents a new type of spin system with local gauge invariance. At each vertex $\xi$ there are $d(d-1)/2$ Ising spins $\Lambda_{\mu,\nu}= \Lambda_{\nu,\mu}$, $\mu \neq \nu = 1,..,d$ and one Ising spin $\Gamma$ on every link $(\xi,\xi +e_{\mu})$. For the frozen spin $\Gamma \equiv 1$ the dual Hamiltonian factorizes into $d(d-1)/2$ two-dimensional Ising ferromagnets and into antiferromagnets in the case $\Gamma \equiv -1$. For fluctuating $\Gamma$ it is a sort of spin glass system with local gauge invariance. The generalization to $p$-branes is given.Comment: 16 pages,Late

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

Geometrical String and Spin Systems

We formulate a new geometrical string on the euclidean lattice. It is possible to find such spin systems with local interaction which reproduce the same surface dynamics.In the three-dimensional case this spin system is a usual Ising ferromagnet with additional diagonal antiferromagnetic interaction and with specially adjusted coupling constants. In the four-dimensional case the spin system coincides with the gauge Ising system with an additional double-plaquette interaction and also with specially tuned coupling constants. We extend this construction to random walks and random hypersurfaces (membrane and p-branes) of high dimensionality. We compare these spin systems with the eight-vertex model and BNNNI models.Comment: 10 pages, Latex,Crete-TH-5-July-199

Self-Avoiding Gonihedric Srting and Spin Systems

We classify different theories of self-intersecting random surfaces assigning special weights to intersections. When self-intersection coupling constant $\kappa$ tends to zero, then the surface can freely inetrsect and it is completely self-avoiding when $\kappa$ tends to infinity. Equivalent spin systems for this general case were constructed. In two-dimension the system with $\kappa = 0$ is in complete disorder as it is in the case of 2D gauge Ising system.Comment: Preprint CRETE-TH-21, October 1993,8 pages,Late

Superstring with Extrinsic Curvature Action

We suggest supersymmetric extension of conformally invariant string theory which is exclusively based on extrinsic curvature action. At the classical level this is a tension-less string theory. The absence of conformal anomaly in quantum theory requires that the space-time should be 6-dimensional.Comment: 10 pages, LaTex, 1 figur

Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings

The correspondences proposed previously between higher spin gauge theories and free singleton field theories were recently extended into a more complete picture by Klebanov and Polyakov in the case of the minimal bosonic theory in D=4 to include the strongly coupled fixed point of the 3d O(N) vector model. Here we propose an N=1 supersymmetric version of this picture. We also elaborate on the role of parity in constraining the bulk interactions, and in distinguishing two minimal bosonic models obtained as two different consistent truncations of the minimal N=1 model that retain the scalar or the pseudo-scalar field. We refer to these models as the Type A and Type B models, respectively, and conjecture that the latter is holographically dual to the 3d Gross-Neveu model. In the case of the Type A model, we show the vanishing of the three-scalar amplitude with regular boundary conditions. This agrees with the O(N) vector model computation of Petkou, thereby providing a non-trivial test of the Klebanov-Polyakov conjecture.Comment: 30p

Certain aspects of regularity in scalar field cosmological dynamics

We consider dynamics of the FRW Universe with a scalar field. Using Maupertuis principle we find a curvature of geodesics flow and show that zones of positive curvature exist for all considered types of scalar field potential. Usually, phase space of systems with the positive curvature contains islands of regular motion. We find these islands numerically for shallow scalar field potentials. It is shown also that beyond the physical domain the islands of regularity exist for quadratic potentials as well.Comment: 15 pages with 4 figures; typos corrected, final version to appear in Regular and Chaotic Dynamic

Renormalized Wick expansion for a modified PQCD

The renormalization scheme for the Wick expansion of a modified version of the perturbative QCD introduced in previous works is discussed. Massless QCD is considered, by implementing the usual multiplicative scaling of the gluon and quark wave functions and vertices. However, also massive quark and gluon counter-terms are allowed in this mass less theory since the condensates are expected to generate masses. A natural set of expansion parameters of the physical quantities is introduced: the coupling itself and to masses $m_q$ and $m_g$ associated to quarks and gluons respectively. This procedure allows to implement a dimensional transmutation effect through these new mass scales. A general expression for the new generating functional in terms of the mass parameters $m_q$ and $m_g$ is obtained in terms of integrals over arbitrary but constant gluon or quark fields in each case. Further, the one loop potential, is evaluated in more detail in the case when only the quark condensate is retained. This lowest order result again indicates the dynamical generation of quark condensates in the vacuum.Comment: 13 pages, one figur