Thomas Spencer (mathematical physicist)

Main Results

• Together with James Glimm and Arthur Jaffe he invented the cluster expansion approach to quantum field theory that is widely used in constructive field theory.
• Together with Jürg Fröhlich and Barry Simon, he invented the approach of the infrared bound, which has now become a classical tool to derive phase transitions in various models of statistical mechanics.
• Together with Jürg Fröhlich, he devised a 'multi-scale analysis' to provide, for the first time, mathematical proofs of: the Kosterlitz–Thouless transition, the phase transition in the one-dimensional ferromagnetic Ising model with interactions and Anderson localization in arbitrary dimension.
• Together with David Brydges, he proved that the scaling limit of the self-avoiding walk in dimension greater or equal than 5 is Gaussian, with variance growing linearly in time. To achieve this result, they invented the technique of the lace expansion that since then has had wide application in probability on graphs.