We study the continuum limit of the spin-1 chain in the non-Abelian bosonization approach of Affleck and show that the Hamiltonian of integrable spin-1 chain yields the Lagrangian of supersymmetric sine-Gordon model in the zero lattice spacing limit. We also show that the quantum group generators of the spin-1 chain give non-local charges of the supersymmetric sine-Gordon theory. PACS numbers: ...

We extend previous work on nite-size eeects with dynamical staggered quarks to the quenched approximation. We again emphasize the large volume limit that is of interest for spectrum calculations which may hope to approach the experimental values. Relying on new calculations at 6=g 2 = 5:7 and recent work with weaker couplings, we extrapolate to the continuum limit and nd a nucleon to rho mass r...

We investigate the dependence of the CP 3 model and of the SU(2) Yang-Mills theory on the vacuum angle. The CP 3 model exhibits a rst order deconnning phase transition in. The critical value of runs from in the strong coupling limit towards zero as is taken to innnity. Qualitatively the same behavior is found in the SU(2) Yang-Mills theory in four dimensions. We discuss the renormalization grou...

We study a single quantum particle in discrete spacetime evolving in a causal way. We see that in the continuum limit any massless particle with a two dimensional internal degree of freedom obeys the Weyl equation, provided that we perform a simple relabeling of the coordinate axes or demand rotational symmetry in the continuum limit. It is surprising that this occurs regardless of the specific...

We consider the Erdős–Rényi random graph G(n, p) inside the critical window, that is when p = 1/n+ λn−4/3, for some fixed λ ∈ R. Then, as a metric space with the graph distance rescaled by n−1/3, the sequence of connected components G(n, p) converges towards a sequence of continuous compact metric spaces. The result relies on a bijection between graphs and certain marked random walks, and the t...

We derive the discrete linear systems associated to multi–matrix models, the corresponding discrete hierarchies and the appropriate coupling conditions. We also obtain the W 1+∞ constraints on the partition function. We then apply to multi– matrix models the technique, developed in previous papers, of extracting hierarchies of differential equations from lattice ones without passing through a c...

In various areas of modern physics and in particular in quantum gravity or foundational space-time physics it is of great importance to be in the possession of a systematic procedure by which a macroscopic or continuum limit can be constructed from a more primordial and basically discrete underlying substratum, which may behave in a quite erratic and irregular way. We develop such a framework w...