Tom Kennedy's Home Page

Office hours

Department of Mathematics

University of Arizona

PRESENT COURSES

FALL '08 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QUANTUM SPIN SYSTEMS BIBLIOGRAPHY (Seriously out of date)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

HOW TO CONTACT ME

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).
2. Debye-Huckel theory for charge symmetric Coulomb systems. Commun. Math. Phys. 92, 269-294 (1983).
3. Mean field theory for Coulomb systems. J. Stat. Phys. 37, 529-559 (1984).
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).
6. Symmetry breaking in the lattice abelian Higgs model (with Chris King). Phys. Rev. Let. 55, 776-778 (1985) .
7. Spontaneous symmetry breakdown in the abelian Higgs model (with Chris King). Commun. Math. Phys. 104, 327-347 (1986).
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).
10. Rigorous results on valence-bond ground states in antiferromagnets (with Ian Affleck, Elliott Lieb, Hal Tasaki). Phys. Rev. Let. 59, 799-802 (1987).
11. Proof of the Peierls instability in one dimension (with Elliott Lieb). Phys. Rev. Let. 59, 1309-1312 (1987)
12. Valence-bond ground states in isotropic quantum antiferromagnets (with Ian Affleck, Elliott Lieb, Hal Tasaki). Commun. Math. Phys. 115, 477-528 (1988).
13. A two dimensional isotropic quantum antiferromagnet with unique disordered ground state (with Elliott Lieb, Hal Tasaki). J. Stat. Phys. 53, 383 (1988).
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).
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).
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).
18. Spin-Peierls transitions in $S>1/2$ Heisenberg chains (with Dandan Guo and Sumit Mazumdar). Phys. Rev. B 41, 9592 (1990).
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).
20. Hidden $Z_2\times Z_2$ symmetry breaking in Haldane gap antiferromagnets (with Hal Tasaki). Phys. Rev. B 45, 304 (1992).
21. Hidden symmetry breaking and the Haldane phase in $S=1$ quantum spin chains (with Hal Tasaki). Commun. Math. Phys. 147 431-484 (1992).
22. Solutions of the Yang-Baxter equation for isotropic quantum spin chains. J. Phys. A: Math. Gen. 25, 2809 (1992).
23. Some rigorous results on majority rule renormalization group transformations near the critical point. J. Stat. Phys. 72, 15-37 (1993).
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).
26. Nonpositive matrix elements for Hamiltonians of spin 1 chains. J. Phys.: Condens. Matter 6, 8015-8022 (1994).
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).
28. Majority Rule at Low Temperatures for the Square Lattice with b=2 and for the Triangular Lattice. J. Stat. Phys. 86, 1089-1107 (1997) Abstract and paper (from arXiv.org).
29. Phase separation in the neutral Falicov-Kimball model. J. Stat. Phys. 91, 829-843 (1998) Abstract and paper (from arXiv.org).
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).
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).
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),
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).
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).
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).
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).
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).
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).
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).

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.