- Main Results
- References
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.[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]
References
1. ^1 IAS website
2. ^APS website
3. ^1991 Dannie Heineman Prize for Mathematical Physics Recipient, American Physical Society. Accessed June 24, 2011
4. ^{{cite journal|first1=J|last1=Glimm|last2=Jaffe|first2=A|last3=Spencer|first3=T|title=The Wightman axioms and particle structure in the
quantum field model|journal=Ann. of Math|year=1974|volume=100|issue=3|pages=585–632|jstor=1970959|doi=10.2307/1970959}}
5. ^{{cite journal|last1=Fröhlich|first1=J.|last2=Simon|first2=B.|last3=Spencer|first3=T.|title=Infrared bounds, phase transitions and continuous symmetry breaking|journal=Comm. Math. Phys.|volume=50|issue=1|year=1976|pages=79–95|doi=10.1007/bf01608557|bibcode = 1976CMaPh..50...79F |citeseerx=10.1.1.211.1865}}
6. ^{{cite journal|last1=Fröhlich|first1=J.|last2=Spencer|first2=T.|title=The Kosterlitz–Thouless transition in two-dimensional abelian spin systems and the Coulomb gas|journal=Comm. Math. Phys.|year=1981|volume=81|issue=4|pages=527–602|url=http://projecteuclid.org/euclid.cmp/1103920388|doi=10.1007/bf01208273|bibcode = 1981CMaPh..81..527F }}
7. ^{{cite journal|last1=Fröhlich|first1=J.|last2=Spencer|first2=T.|title=The phase transition in the one-dimensional Ising model with 1/r2 interaction energy.|journal=Comm. Math. Phys.|year=1982|volume=84|issue=1|pages=87–101|doi=10.1007/BF01208373|bibcode = 1982CMaPh..84...87F }}
8. ^{{cite journal|last1=Fröhlich|first1=J.|last2=Spencer|first2=T.|title=Absence of diffusion in the Anderson tight binding model for large disorder or low energy.|journal=Comm. Math. Phys.|year=1983|volume=88|issue=2|pages=151–184|url=http://projecteuclid.org/getRecord?id=euclid.cmp/1103922279|doi=10.1007/bf01209475|bibcode = 1983CMaPh..88..151F }}
9. ^{{cite journal|last1=Brydges|first1=D.|last2=Spencer|first2=T.|title=Self-avoiding walk in 5 or more dimensions|journal=Comm. Math. Phys.|year=1985|volume=97|issue=1–2|pages=125–148|url=http://projecteuclid.org/euclid.cmp/1103941982|doi=10.1007/bf01206182|bibcode = 1985CMaPh..97..125B }}
10. ^{{cite book|last1=Slade|first1=G.|title=The lace expansion and its applications |series=Lecture Notes in Mathematics|volume=1879| publisher=Springer|year=2006|url=https://www.springer.com/mathematics/probability/book/978-3-540-31189-8|isbn=9783540311898}}
{{Authority control}}{{DEFAULTSORT:Spencer, Thomas}}{{US-mathematician-stub}}2. ^APS website
3. ^1991 Dannie Heineman Prize for Mathematical Physics Recipient, American Physical Society. Accessed June 24, 2011
4. ^{{cite journal|first1=J|last1=Glimm|last2=Jaffe|first2=A|last3=Spencer|first3=T|title=The Wightman axioms and particle structure in the
quantum field model|journal=Ann. of Math|year=1974|volume=100|issue=3|pages=585–632|jstor=1970959|doi=10.2307/1970959}}5. ^{{cite journal|last1=Fröhlich|first1=J.|last2=Simon|first2=B.|last3=Spencer|first3=T.|title=Infrared bounds, phase transitions and continuous symmetry breaking|journal=Comm. Math. Phys.|volume=50|issue=1|year=1976|pages=79–95|doi=10.1007/bf01608557|bibcode = 1976CMaPh..50...79F |citeseerx=10.1.1.211.1865}}
6. ^{{cite journal|last1=Fröhlich|first1=J.|last2=Spencer|first2=T.|title=The Kosterlitz–Thouless transition in two-dimensional abelian spin systems and the Coulomb gas|journal=Comm. Math. Phys.|year=1981|volume=81|issue=4|pages=527–602|url=http://projecteuclid.org/euclid.cmp/1103920388|doi=10.1007/bf01208273|bibcode = 1981CMaPh..81..527F }}
7. ^{{cite journal|last1=Fröhlich|first1=J.|last2=Spencer|first2=T.|title=The phase transition in the one-dimensional Ising model with 1/r2 interaction energy.|journal=Comm. Math. Phys.|year=1982|volume=84|issue=1|pages=87–101|doi=10.1007/BF01208373|bibcode = 1982CMaPh..84...87F }}
8. ^{{cite journal|last1=Fröhlich|first1=J.|last2=Spencer|first2=T.|title=Absence of diffusion in the Anderson tight binding model for large disorder or low energy.|journal=Comm. Math. Phys.|year=1983|volume=88|issue=2|pages=151–184|url=http://projecteuclid.org/getRecord?id=euclid.cmp/1103922279|doi=10.1007/bf01209475|bibcode = 1983CMaPh..88..151F }}
9. ^{{cite journal|last1=Brydges|first1=D.|last2=Spencer|first2=T.|title=Self-avoiding walk in 5 or more dimensions|journal=Comm. Math. Phys.|year=1985|volume=97|issue=1–2|pages=125–148|url=http://projecteuclid.org/euclid.cmp/1103941982|doi=10.1007/bf01206182|bibcode = 1985CMaPh..97..125B }}
10. ^{{cite book|last1=Slade|first1=G.|title=The lace expansion and its applications |series=Lecture Notes in Mathematics|volume=1879| publisher=Springer|year=2006|url=https://www.springer.com/mathematics/probability/book/978-3-540-31189-8|isbn=9783540311898}}
5 : 1946 births|Living people|Mathematical physicists|Members of the United States National Academy of Sciences|Institute for Advanced Study faculty
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