[en] We analyze with the background field method the ratio of the renormalization group scales in the continuum Λsub(cont) and on the lattice Λsub(L). We find in contrast to an earlier background field calculation good agreement with conventional calculations, extend the result in analytic form to any acceptable lattice action and find actions where the ratio can take any value. Comparison with available computer data is made. Qualitative agreement is found

[en] The exact solution of the Blume-Emery-Griffiths model on the Bethe lattice was studied in the subspace K = -In coshJ. 11 refs

[en] The semi-analytic method of plaquette expansion is briefly reviewed, and results of applications to Hamiltonian lattice field theory summarized

[en] We review the theoretical basis and the possible applications of Symanzik's improvement program. We discuss also how the program may be extended in such a way to become compatible with the Osterwalder-Schrader positivity. (orig.)

No abstract available

[en] The relations between integrable systems and conformal field theories have first been worked out in the continuum limit. Using Coulomb gas and Bethe ansatz techniques, critical exponents and partition functions were obtained for various lattice models giving exact results of practical interest as well as a precise correspondence with conformal theories. It was later realized that the two subjects exhibit numerous similarities, and although this is maybe unexpected a priori, that some prints of the conformal invariant structure are present on the lattice before the continuum limit. We review here recent progress on this question

[en] This talk is a report on results obtained by T. Jolicoeur, R. Lacaze, B. Petersson and the author: staggered fermions can be consistently interpreted as flavoured quarks in the continuum limit of asymptotically free theories on the lattice. This statement is supported by analytical results for the Gross-Neveu model at large N and for a QCD two point function, and by a numerical simulation of SU(2) quenched QCD

[en] Short communication

[en] The d-simplex equations are multidimensional generalizations of the Yang-Baxter (triangle) equations. We discuss the algebraic structure of the hierarchy of the d-simplex equations and their relevance to the notion of quantum and classical integrability. A multidimensional generalization of the notion of lax pair is given. 7 refs

[en] The antiferromagnetic Potts model in the magnetic field is rigorously considered on the Bethe lattice by means of recursion relation. This allows one to study critical properties of the model as properties of iteration sequence { x_n } in limit n → ∼. We observe the line of second order phase transition, taking place as a period doubling bifurcations of recursive sequence. 12 refs