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\centerline{\bf Simulating Spin Models on the Connection Machine}

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\centerline{Zheng-Yao Su}
\centerline{Physics Department}
\centerline{Syracuse University}
% \centerline{Paul Coddington, Physics Department, Syracuse University}

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The study of spin models not only has provided insights to the general theory of
phase transitions and critical phenomena, but also has been proposed
(for example by Geoffrey Fox) 
to be an alternative approach to certain types of complex systems,
especially the model we are tackling, which is highly inhomogeneous, in 
contrast to the traditionally homogeneous spin models. 
A number of interesting conjectures are waiting to be verified and 
novel discoveries are expected to be seen from this model. 
In addition, this research is going to develop new techniques probing
the potential connections between the well known statistical mechanical theories
and the ubiquitous behaviours existing in nonlinear dynamics.  

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Much of our understanding of spin models comes from computer simulations 
using Monte Carlo methods. We have implemented a Monte Carlo algorithm 
for the inhomogeneous Ising model on the Connection Machine, and
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have successfully built a visualization 
environment to display the evolution of the spins on an Xwindow of a remote
terminal. This environment is intentionally designed to be flexible, so that
a wide spectrum of interactions for several different spin models
can be easily implemented. 
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Furthermore, not sacrificed by this flexibility,
the efficiency of the code is 80\% to 90\% of CM active time, 
depending on the interactions.
However, due to the extremely time-consuming nature of Monte Carlo algorithms,
one or two hundred hours of time on the CM is a conservative estimate to 
complete a good description of 
a system with one particular set of interactions 
for one spin model. Accordingly, 1000
hours of computational time on the CM should be a circumspect request to 
investigate about 5-10 different types of interactions for one model. 
This research would greatly benefit by the use of
the SUN front-end, {\it swan}. 
Compared with the VAX machine, {\it cmx}, in current use, {\it swan} will
drastically reduce the I/O time and will thereby accelerate the data 
transfer and especially the graphics display, which is an essential
element of this research. 

Part of this project will be done in collaboration with Dr. Paul Coddington. 
He has been working on the development of parallel versions of the new 
``cluster'' algorithms which are non-local, updating clusters of spins at a 
time, rather than single spins as in the conventional Monte Carlo methods. 
So far cluster algorithms have only been applied to homogeneous spin models,
where they dramatically reduce critical slowing down, and consequently can
greatly improve the Monte Carlo simulation.
We are very interested in whether these new algorithms work well on 
inhomogeneous problems, and also in developing more efficient parallel cluster
algorithms for the Connection Machine.
In particular, due to the native multifractal characteristics of cluster 
algorithms, this approach should give us some inspiration in studying the 
aforementioned relation between statistical physics and nonlinear dynamics. 
   

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