Thomas Spencer (mathematical physicist)

Thomas C. Spencer
Born	December 24, 1946 (1946-12-24) (age 78)
Education	AB, University of California, Berkeley PhD, New York University
Employer	Institute for Advanced Study
Title	Professor
Spouse	Bridget Murphy
Awards	Henri Poincaré Prize (2015) Dannie Heineman Prize for Mathematical Physics (1991)

Thomas C. Spencer (born December 24, 1946) is an American mathematical physicist, known in particular for important contributions to constructive quantum field theory, statistical mechanics, and spectral theory of random operators. He is an emeritus faculty member at the Institute for Advanced Study. ^[1]

Career

Spencer earned his doctorate in 1972 from New York University with a dissertation titled Perturbation of the Po2 Quantum Field Hamiltonian written under the direction of James Glimm. Since 1986, he has been a faculty member in the School of Mathematics at the Institute for Advanced Study.^{[ citation needed ]}

Research

• 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. ^[2]
• 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. ^[3]
• Together with Jürg Fröhlich, he devised a 'multi-scale analysis' to provide, for the first time, mathematical proofs of: the Kosterlitz–Thouless transition, ^[4] the phase transition in the one-dimensional ferromagnetic Ising model with interactions ${\displaystyle J_{x,y}\sim |x-y|^{-2}}$ ^[5] and Anderson localization in arbitrary dimension. ^[6]
• 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. ^[7] To achieve this result, they invented the technique of the lace expansion that since then has had wide application in probability on graphs. ^[8]

Awards and honors

Spencer is a member of the United States National Academy of Sciences, ^[1] and the recipient of the Dannie Heineman Prize for Mathematical Physics (joint with Jürg Fröhlich, "For their joint work in providing rigorous mathematical solutions to some outstanding problems in statistical mechanics and field theory."). ^{[9] [10]}

References

1. IAS website
2. Glimm, J; Jaffe, A; Spencer, T (1974). "The Wightman axioms and particle structure in the ${\displaystyle P(\phi )_{2}}$ quantum field model". Ann. of Math. 100 (3): 585–632. doi:10.2307/1970959. JSTOR   1970959.
3. Fröhlich, J.; Simon, B.; Spencer, T. (1976). "Infrared bounds, phase transitions and continuous symmetry breaking". Comm. Math. Phys. 50 (1): 79–95. Bibcode:1976CMaPh..50...79F. CiteSeerX   10.1.1.211.1865 . doi:10.1007/bf01608557. S2CID   16501561.
4. Fröhlich, J.; Spencer, T. (1981). "The Kosterlitz–Thouless transition in two-dimensional abelian spin systems and the Coulomb gas". Comm. Math. Phys. 81 (4): 527–602. Bibcode:1981CMaPh..81..527F. doi:10.1007/bf01208273. S2CID   73555642.
5. Fröhlich, J.; Spencer, T. (1982). "The phase transition in the one-dimensional Ising model with 1/r² interaction energy". Comm. Math. Phys. 84 (1): 87–101. Bibcode:1982CMaPh..84...87F. doi:10.1007/BF01208373. S2CID   122722140.
6. Fröhlich, J.; Spencer, T. (1983). "Absence of diffusion in the Anderson tight binding model for large disorder or low energy". Comm. Math. Phys. 88 (2): 151–184. Bibcode:1983CMaPh..88..151F. doi:10.1007/bf01209475. S2CID   121435596.
7. Brydges, D.; Spencer, T. (1985). "Self-avoiding walk in 5 or more dimensions" . Comm. Math. Phys. 97 (1–2): 125–148. Bibcode:1985CMaPh..97..125B. doi:10.1007/bf01206182. S2CID   189832287.
8. Slade, G. (2006). The lace expansion and its applications. Lecture Notes in Mathematics. Vol. 1879. Springer. ISBN   9783540311898.
9. APS website
10. 1991 Dannie Heineman Prize for Mathematical Physics Recipient, American Physical Society. Accessed June 24, 2011