A REVIEW OF THE LARGE N LIMIT OF TENSOR MODELS

N. Limić

Valentin Bonzom

János Kertész, Dietrich Stauffer

Lattices up to size 6400*6400 are simulated on a 32-processor Intel Hypercube parallel computer. At the critical temperature of the square-lattice Ising model, the magnetization decays roughly exponentially with time if we start with all spins parallel and if the lattice is large enough. This result is consistent with those of Heermann and Burkitt.

S. MILOŠEVIj, Eugene Stanley

The spherical model can be regarded either as an exactly-soluble approximation to the Ising model or as a model of isotropically interacting spins in which the spin dimensionality ν approaches infinity. In this note we calculate 80 terms in the high-temperature expansions for the spherical model and compare with predictions which would have been obtained if only ~ 10 terms were known (as in the case for finite ν). We find that the critical point exponents deduced from short series are extremely doubtful when d > 3, where d is the lattice dimensionality. In particular, we note that it is quite possible that the mean field exponents are valid for all ν if d > 3.

Valentin Bonzom

Razvan Gurău

Matrix models are a highly successful framework for the analytic study of random two dimensional surfaces with applications to quantum gravity in two dimensions, string theory, conformal field theory, statistical physics in random geometry, etc. Their success relies crucially on the so called 1/N expansion introduced by 't Hooft. In higher dimensions matrix models generalize to tensor models. In the absence of a viable 1/N expansion tensor models have for a long time been less successful in providing an analytically controlled theory of random higher dimensional topological spaces. This situation has drastically changed recently. Models for a generic complex tensor have been shown to admit a 1/N expansion dominated by graphs of spherical topology in arbitrary dimensions and to undergo a phase transition to a continuum theory.