Thomas C. Spencer | |
---|---|

Born | December 24, 1946 75) | (age

Education | A.B., University of California, Berkeley Ph.D., New York University |

Employer | Institute for Advanced Study |

Title | Professor |

Spouse(s) | 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.^{ [1] } He earned his doctorate in 1972 from New York University with a dissertation entitled *Perturbation of the Po2 Quantum Field Hamiltonian* written under the direction of James Glimm. Since 1986, he has been professor of mathematics at the Institute for Advanced Study. He 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.*").^{ [2] }^{ [3] }

- 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.
^{ [4] } - 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.
^{ [5] }

- Together with Jürg Fröhlich, he devised a 'multi-scale analysis' to provide, for the first time, mathematical proofs of: the Kosterlitz–Thouless transition,
^{ [6] }the phase transition in the one-dimensional ferromagnetic Ising model with interactions^{ [7] }and Anderson localization in arbitrary dimension.^{ [8] } - 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.
^{ [9] }To achieve this result, they invented the technique of the lace expansion that since then has had wide application in probability on graphs.^{ [10] }

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- 1 2 IAS website
- ↑ APS website
- ↑ 1991 Dannie Heineman Prize for Mathematical Physics Recipient, American Physical Society. Accessed June 24, 2011
- ↑ Glimm, J; Jaffe, A; Spencer, T (1974). "The Wightman axioms and particle structure in the quantum field model".
*Ann. of Math*.**100**(3): 585–632. doi:10.2307/1970959. JSTOR 1970959. - ↑ 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. - ↑ 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. - ↑ Fröhlich, J.; Spencer, T. (1982). "The phase transition in the one-dimensional Ising model with 1/
*r*^{2}interaction energy".*Comm. Math. Phys*.**84**(1): 87–101. Bibcode:1982CMaPh..84...87F. doi:10.1007/BF01208373. S2CID 122722140. - ↑ 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. - ↑ 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. - ↑ Slade, G. (2006).
*The lace expansion and its applications*. Lecture Notes in Mathematics. Vol. 1879. Springer. ISBN 9783540311898.

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