Tom Kennedy's Home Page

Office hours

Department of Mathematics

University of Arizona

HOW TO CONTACT ME

FALL '09 COURSES

CODE FOR SIMULATING CHORDAL SLE (fast_sle)

CODE FOR SIMULATING SELF-AVOIDING WALKS

PICTURES OF CHORDAL SLE - NEW updated 12/16/2005

PICTURES OF SELF-AVOIDING WALKS

PACKING THE PLANE WITH 2 SIZES OF DISCS

Pictures and non-rigorous results on the problem of what is the densest packing of the plane using discs of radius 1 and r.

QUANTUM SPIN SYSTEMS BIBLIOGRAPHY (Seriously out of date)

A bibliography of mathematically rigorous results on quantum spins systems with links to various archives. Maintained by TK and Bruno Nachtergaele.

PAST COURSES

EDUCATION

EMPLOYMENT

GRADUATE STUDENTS

Past students

• Martin Pokorny
• Karl Haller

Current students

• Ben Dyhr

PUBLICATIONS

1. A lower bound on the partition function for a classical charge symmetric system. J. Stat. Phys. 28, 633-638 (1982).
   Paper online in J. Stat. Phys. (from springlink.com).
2. Debye-Huckel theory for charge symmetric Coulomb systems. Commun. Math. Phys. 92, 269-294 (1983).
   Paper online in Commun. Math. Phys. (from springlink.com).
3. Mean field theory for Coulomb systems. J. Stat. Phys. 37, 529-559 (1984).
   Paper online in J. Stat. Phys. (from springlink.com).
4. Long range order in the anisotropic quantum ferromagnetic Heisenberg model. Commun. Math. Phys. 100, 447-462 (1985).
   Paper online in Commun. Math. Phys. (from springlink.com).
5. Surface effects in Debye screening (with Paul Federbush). Commun. Math. Phys. 102, 361-423 (1985).
   Paper online in Commun. Math. Phys. (from springlink.com).
6. Symmetry breaking in the lattice abelian Higgs model (with Chris King). Phys. Rev. Let. 55, 776-778 (1985) .
   Paper online in Physical Review Letters (from Physical Review Online Archive.
7. Spontaneous symmetry breakdown in the abelian Higgs model (with Chris King). Commun. Math. Phys. 104, 327-347 (1986).
   Paper online in Commun. Math. Phys. (from springlink.com).
8. An itinerant electron model with crystalline or magnetic long range order (with Elliott Lieb). Physica 138A, 320-358 (1986).
9. Mayer expansions and the Hamilton-Jacobi equation (with David Brydges). J. Stat. Phys. 48, 19-49, (1987).
   Paper online in J. Stat. Phys. (from springlink.com).
10. Rigorous results on valence-bond ground states in antiferromagnets (with Ian Affleck, Elliott Lieb, Hal Tasaki). Phys. Rev. Let. 59, 799-802 (1987).
    Paper online in Physical Review Letters (from Physical Review Online Archive.
11. Proof of the Peierls instability in one dimension (with Elliott Lieb). Phys. Rev. Let. 59, 1309-1312 (1987)
    Paper online in Physical Review Letters (from Physical Review Online Archive.
12. Valence-bond ground states in isotropic quantum antiferromagnets (with Ian Affleck, Elliott Lieb, Hal Tasaki). Commun. Math. Phys. 115, 477-528 (1988).
    Paper online in Commun. Math. Phys. (from springlink.com).
13. A two dimensional isotropic quantum antiferromagnet with unique disordered ground state (with Elliott Lieb, Hal Tasaki). J. Stat. Phys. 53, 383 (1988).
    Paper online in J. Stat. Phys. (from springlink.com).
14. Existence of N\'eel order in some spin 1/2 Heisenberg antiferromagnets (with Elliott Lieb, B. Sriram Shastry). J. Stat. Phys. 53, 1019 (1988).
    Paper online in J. Stat. Phys. (from springlink.com).
15. The XY model has long-range order for all spins and all dimensions greater than one (with Elliott Lieb, B. Sriram Shastry). Phys. Rev. Let. 61 2582 (1988).
    Paper online in Physical Review Letters (from Physical Review Online Archive.
16. A fixed point equation for the high temperature phase of discrete lattice spin systems. J. Stat. Phys. 59, 195-220 (1990).
    Paper online in J. Stat. Phys. (from springlink.com).
17. Exact diagonalization of open spin 1 chains. J. Phys.: Condens. Matter 2, 5737-5745 (1990).
    Paper online in J. Phys. Condens. Matter (from iop.org).
18. Spin-Peierls transitions in $S>1/2$ Heisenberg chains (with Dandan Guo and Sumit Mazumdar). Phys. Rev. B 41, 9592 (1990).
    Paper online in Physical Review B (from Physical Review Online Archive.
19. Ornstein-Zernike decay in the ground state of the quantum Ising model in a transverse magnetic field. Commun. Math. Phys. 137, 599-615 (1991).
    Paper online in Commun. Math. Phys. (from springlink.com).
20. Hidden $Z_2\times Z_2$ symmetry breaking in Haldane gap antiferromagnets (with Hal Tasaki). Phys. Rev. B 45, 304 (1992).
    Paper online in Physical Review B (from Physical Review Online Archive.
21. Hidden symmetry breaking and the Haldane phase in $S=1$ quantum spin chains (with Hal Tasaki). Commun. Math. Phys. 147 431-484 (1992).
    Paper online in Commun. Math. Phys. (from springlink.com).
22. Solutions of the Yang-Baxter equation for isotropic quantum spin chains. J. Phys. A: Math. Gen. 25, 2809 (1992).
    Paper online in J. Phys. A (from iop.org).
23. Some rigorous results on majority rule renormalization group transformations near the critical point. J. Stat. Phys. 72, 15-37 (1993).
    Paper online in J. Stat. Phys. (from springlink.com).
24. Some rigorous results on the ground states of the Falicov-Kimball model. Rev. Math. Phys. 6 901-925 (1994). Also in The State of Matter , Michael Aizenman and Huzihiro Araki (eds.) World Scientific, 1994.
    Abstract (from Texas archive), Paper (from Texas archive).
25. Ballistic behavior in a 1-d weakly self-avoiding walk with decaying energy penalty. J. Stat. Phys. 77, 565-579 (1994).
    Paper online in J. Stat. Phys. (from springlink.com).
26. Nonpositive matrix elements for Hamiltonians of spin 1 chains. J. Phys.: Condens. Matter 6, 8015-8022 (1994).
    Paper online in J. Phys. Condens. Matter (from iop.org).
27. Absence of renormalization group pathologies near the critical temperature - two examples (with Karl Haller). J. Stat. Phys. 85, 607-637 (1996).
    Abstract (from Texas archive), Paper (from Texas archive).
    Paper online in J. Stat. Phys. (from springlink.com).
28. Majority Rule at Low Temperatures on the square and triangular lattices. J. Stat. Phys. 86, 1089-1107 (1997)
    Abstract and paper (from arXiv.org).
    Paper online in J. Stat. Phys. (from springlink.com).
29. Phase separation in the neutral Falicov-Kimball model. J. Stat. Phys. 91, 829-843 (1998)
    Abstract and paper (from arXiv.org).
    Paper online in J. Stat. Phys. (from springlink.com).
30. Periodic Ground States in the Neutral Falicov-Kimball Model in Two Dimensions (with Karl Haller). J. Stat. Phys. 102, 15-34 (2001)
    Abstract and paper (from arXiv.org).
    Paper online in J. Stat. Phys. (from springlink.com).
31. A faster implementation of the pivot algorithm for self-avoiding walks. J. Stat. Phys. 106, 407-429 (2002)
    Abstract and paper (from arXiv.org).
    Paper online in J. Stat. Phys. (from springlink.com).
32. Expansions for one quasiparticle states in spin 1/2 systems (with Nilanjana Datta). J. Stat. Phys. 108, 373-399 (2002)
    Abstract and paper (from arXiv.org),
    Paper online in J. Stat. Phys. (from springlink.com).
33. Monte Carlo tests of SLE predictions for the 2D self-avoiding walk. Phys. Rev. Lett. 88, 130601 (2002)
    Abstract and paper (from arXiv.org).
    Paper online in Physical Review Letters (from Physical Review Online Archive.
34. Conformal invariance and stochastic Loewner evolution predictions for the 2D self-avoiding walk - Monte Carlo tests, J. Stat. Phys. 114, 51-78 (2004)
    Abstract and paper (from arXiv.org).
    Paper online in J. Stat. Phys. (from springlink.com).
35. Instability of interfaces in the antiferromagnetic XXZ chain at zero temperature (with Nilanjana Datta). Commun. Math.Phys. 236 , 477 (2003)
    Abstract and paper (from arXiv.org).
    Paper online in Commun. Math. Phys. (from springlink.com).
36. Expansions for Droplet States in the Ferromagnetic XXZ Heisenberg Chain, Markov Processes and Related Fields. 11 , 223 (2005)
    Abstract and paper (from arXiv.org).
37. Compact packings of the plane with two sizes of discs, Discrete and Computational Geometry 35, 255-267 (2006).
    Abstract and paper (from arXiv.org).
    Paper online in Discrete and Computational Geometry (from springlink.com).
38. A densest compact planar packing with two sizes of discs, (2004),
    Abstract and paper (from arXiv.org).
39. A fast algorithm for simulating the chordal Schramm-Loewner evolution, J. Stat. Phys. 128, 1125-1137 (2007).
    Abstract and paper (from arXiv.org).
    Paper online in J. Stat. Phys. (from springlink.com).
40. Monte Carlo comparisons of the self-avoiding walk and SLE as parameterized curves (2005),
    Abstract and paper (from arXiv.org).
41. The length of an SLE - Monte Carlo studies, J. Stat. Phys. 128, 1263-1277 (2007).
    Abstract and paper (from arXiv.org).
    Paper online in J. Stat. Phys. (from springlink.com).
42. Computing the Loewner driving process of random curves in the half plane, J. Stat. Phys. 131, 803-819 (2008).
    Abstract and paper (from arXiv.org).
    Paper online in J. Stat. Phys. (from springlink.com).
43. Conditioning SLE's and loop erased random walks (with Michel Bauer and Denis Bernard), J. Math. Phys. 50, 043301 (2009).
    Abstract and paper (from arXiv.org). Paper online in J. Math. Phys.
44. Renormalization group maps for Ising models in lattice gas variables. Preprint (2009).
    Abstract and paper (from arXiv.org).
45. Numerical computations for the Schramm-Loewner Evolution. Preprint (2009).
    Abstract and paper (from arXiv.org). Paper online in J. Stat. Phys.

TALKS

1. Monte Carlo comparisons of the self-avoiding walk and SLE - How should SLE be parameterized? BIRS, Banff, March 15, 2005
2. Monte Carlo comparisons of the self-avoiding walk and SLE - How should SLE be parameterized? 93rd Statistical Mechanics Conference, Rutgers University, May 15, 2005
3. Monte Carlo comparisons of the self-avoiding walk and SLE as parameterized curves, Critical Scaling for Polymers and Percolation, Banff International Research Station, May 29, 2005
4. The length of an SLE - Monte Carlo studies, Stochastic Geometry and Field Theory Program, Kavli Institute for Theoretical Physics, September 19, 2006
5. Numerical simulation of random curves, 2008 Enrage Topical School ON GROWTH AND SHAPES, Institute Henri Poincare, Paris, June 2-6, 2008
6. Testing for SLE using the driving process , 13th Itzykson Conference PUZZLES OF GROWTH, Saclay, France, June 9-11, 2008.
7. Monte Carlo Studies of Self-Avoiding Walks and Loops , Stochastic Loewner Evolution and Scaling Limits, CRM, Montreal, Canada, August 4-8, 2008.
8. Renormalization group maps for Ising models in lattice gas variable , The Renormalization Group and Statistical Mechanics, July 6-12, 2009, UBC, Vancouver, Canada.