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\leftline{{\bf  Dr. Paul Coddington   (Research fellow, Prof. Fox's 
group) }}
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The study of spin models of magnetic materials is important not only for
understanding the properties of these materials, but also for the insights
it provides to the general theory of phase transitions and critical
phenomena. Much of our understanding of spin models comes from computer
simulations using Monte Carlo methods. Recently new algorithms have been
introduced which greatly increase the computational efficiency of these
simulations by dramatically reducing critical slowing down, which is the
tendency for the Monte Carlo scheme to take many iterations to produce a
statistically independent data value near the critical point. These new 
"cluster" algorithms allow much larger spin systems to be studied. The 
dynamics of the algorithms themselves are also of great interest.


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\underline{  Research projects for REU participants  }
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There are currently three areas of study which are being pursued. All of
these projects would involve the use of the high performance computers
available at the Northeast Parallel Architecture Center (NPAC).
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1) Parallel cluster algorithms:
Cluster algorithms are non-local, updating clusters of spins at a time,
rather than single spins. The non-locality and irregularity of the clusters
means that unlike the standard local algorithms, the cluster algorithms are
very difficult to implement efficiently on large parallel computers. Some
algorithms have been developed for MIMD machines such as the NCUBE hypercube,
as well as SIMD machines such as the Connection Machine, but much more work
needs to be done to improve the rather poor efficiency of these algorithms.

2) Studying cluster algorithms:
There is very little theoretical knowledge about how cluster algorithms work
so well, and computer simulations allow us to obtain accurate numerical data
to compare different algorithms, and to test any theories of how these
algorithms work. New cluster algorithms are also being investigated, and
programs for visualizing these new algorithms using computer graphics 
are being developed for different models.

3) Physics of spin models:
The cluster algorithms allow us to simulate much larger systems with much
better statistics, thus enabling us to study their properties in greater 
detail. Projects here include studies of phase transitions in Potts models, 
spin glasses, and other frustrated systems. 


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{\large {\bf Paul David Coddington}}
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\leftline{{\bf Education: } }
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1979-82: University of Western Australia, Perth; 
B.Sc. with first class honours in physics, with a double major in
mathematics.
Received prize as the top physics student in 1979 and 1980.
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1983-88: University of Southampton, U.K.,
Ph.D. in theoretical physics, supervised by Prof. A.J.G. Hey.
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Thesis entitled: ``Deconfinement Transitions in Lattice Gauge Theories''
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1988-90: California Institute of Technology; 
Research Fellow in the Physics Department, working in the Caltech Concurrent
Computation Group
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1990-91: Syracuse University,
Research Associate in the Physics Department, and the Northeast Parallel
Architecture Center.

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{\large {\bf  PUBLICATIONS   }}
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1.
P.D. Coddington, A.J.G. Hey, A.A. Middleton and J.S. Townsend,
 ``The Deconfining Transition for Finite Temperature U(1) Lattice
Gauge Theory in $(2+1)$ Dimensions'',
{\it Phys. Lett.} {\bf B175}, 64 (1986).
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2. 
P. Coddington, A. Hey, J. Mandula and M. Ogilvie,
 ``The Lattice Photon Propagator'',
 {\it Phys. Lett.} {\bf B197}, 191 (1987).
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3. 
J.T. Chalker and P.D. Coddington,
 ``Percolation, Quantum Tunneling and the Integer Hall Effect'',
 {\it J. Phys. C} {\bf 21}, 2665 (1988).
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4
P.D. Coddington,
 ``The Application of Transputer Arrays to Scientific Problems'',
 {\it Proceedings of the First Australian Occam User's Group Meeting},
Melbourne (June 1988), J. Hulskamp ed.
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5. 
P.D. Coddington and C.F. Baillie,
 ``A Comparison of Cluster Algorithms for Potts Models'',
 {\it Proc. of the International Workshop `Lattice 89'},
Capri (Sept 1989),
{\it Nucl. Phys. B (Proc. Suppl.)} {\bf 17}, 305 (1990).
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6.
 ``Cluster Algorithms for Spin Models on MIMD Parallel Computers'',
 {\it Proc. of the 5th Distributed Memory Computing Conference},
Charleston (April 1990), eds. D.W. Walker and Q.F. Stout
(IEEE Computer Society Press, Los Alamitos, California, 1990).
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7. 
C.F. Baillie and P.D. Coddington,
 ``Comparison of Cluster Algorithms for 2-D Potts Models'',
  Phys. Rev. B {\bf 43}, 10617 (1991).
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8.
P.D. Coddington and C.F. Baillie,
``Parallel Cluster Algorithms'',
 {\it Proc. of the International Conference on Lattice Field Theory},
 Tallahassee (October 1990),
 {\it Nucl. Phys. B (Proc. Suppl.)} {\bf 20}, 76 (1991).
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9. 
C.F. Baillie and P.D. Coddington,
``Cluster Identification Algorithms for Spin Models --- Sequential and
 Parallel'',
 {\it Concurrency: Practice and Experience} {\bf 3}, 129 (1990).
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10.
J. Apostolakis, P. Coddington and E. Marinari,
``A Multi-Grid Cluster Labeling Scheme'',
 to be published in {\it Europhys. Lett.}
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11.
P.D. Coddington and C.F. Baillie,
``Empirical relations between static and dynamic exponents for
 Ising model cluster algorithms'',
 submitted to {\it Phys. Rev. Lett.}


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