These lectures provides a brief introduction to the theory of critical phenomena, including the Ising and 4 spin models, and the strictly and weakly self-avoiding walk. Then recent results in dimension 4 for the 4 model and the weakly self-avoiding walk are discussed. These results have been obtained using a rigorous renormalisation group method. Several tools that are fundamental to the renormalisation group method are subsequently introduced, including Gaussian integration, perturbative renormalisation, and the ...
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These lectures provides a brief introduction to the theory of critical phenomena, including the Ising and 4 spin models, and the strictly and weakly self-avoiding walk. Then recent results in dimension 4 for the 4 model and the weakly self-avoiding walk are discussed. These results have been obtained using a rigorous renormalisation group method. Several tools that are fundamental to the renormalisation group method are subsequently introduced, including Gaussian integration, perturbative renormalisation, and the stable manifold theorem. The last third of these lectures discusses non-perturbative aspects of the implementation of a renormalisation group step. Tutorials are included.
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