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It is generally taken for granted that two-dimensional critical phenomena can be fully classiied by the well known two-dimensional (rational) conformal quantum eld theories (CQFTs). In particular it is believed that in models with a continuous symmetry characterized by a Lie group G the continuum theory enjoys an enhanced symmetry GG due to the decoupling(More)
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In dimension D ≤ 2 the low temperature behavior of systems enjoying a continuous symmetry is dominated by super-instantons: classical configurations of arbitrarily low energy. Perturbation theory in the background of a super-instanton produces thermodynamic answers for the invariant Green's functions that differ from the standard ones, but only in(More)
In this talk I give an overview of the work done during the last 15 years in collaboration with the late Adrian Patrascioiu. In this work we accumulated evidence against the commonly accepted view that theories with nonabelian symmetry – either two dimensional nonlinear σ models or four dimensional Yang-Mills theories – have the property of asymptotic(More)
Compact (ferro-and antiferromagnetic) sigma-models and noncompact (hy-perbolic) sigma-models are compared in a lattice formulation in dimensions d ≥ 2. While the ferro-and antiferromagnetic models are essentially equivalent , the qualitative difference to the noncompact models is highlighted. The perturbative and the large N expansions are studied in both(More)