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Series Expansions Department of Physics

Summary: .
Series Expansions
Joan Adler
Department of Physics
Technion­IIT, 32000, Haifa, Israel.

There are three general approaches for understanding the critical behavior of systems
that have not been solved exactly. One approach is approximation, e.g., mean­field theory
and real space renormalization group techniques. However, such approximations often are
unreliable in two and three dimensions and are difficult to extend in a controlled manner.
A second approach is computer simulation. Simulations would give exact results if the
system were infinite and if a sufficient number of independent configurations could be
generated. Simulations have had an enormous impact in recent years, but accurate results
often require large computer resources and sophisticated algorithms. In addition, it can be
difficult to determine that a system has reached equilibrium and to extrapolate the results
to the thermodynamic limit. Of course, a simulation is restricted to a particular model in a
given spatial dimension at one time. The third general approach is a controlled expansion
from a limit where the model can be solved exactly. An example is the momentum space
renormalization group method where an expansion is made from a dimension where the


Source: Adler, Joan - Physics Department, Technion, Israel Institute of Technology


Collections: Physics