American mathematical physicist
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]
J
x
,
y
∼ ∼ -->
|
x
− − -->
y
|
− − -->
2
{\displaystyle J_{x,y}\sim |x-y|^{-2}}
[ 5] 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] 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] 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
^ a b IAS website ^ Glimm, J; Jaffe, A; Spencer, T (1974). "The Wightman axioms and particle structure in the
P
(
ϕ ϕ -->
)
2
{\displaystyle P(\phi )_{2}}
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 ISBN 9783540311898 ^ APS website ^ 1991 Dannie Heineman Prize for Mathematical Physics Recipient , American Physical Society . Accessed June 24, 2011
International National Academics Other
