A S'tring Theory Approach To the Three- Dimensionai Ising Model
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Date
1989-06
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Addis Ababa University
Abstract
The thre(!"-d"lmctlsional ISing mode"' (3DII~) hilS been Olie td
the unsolved problems in physics. Polyakov hiS sugg0sted ~hlt
It may be possible to solve this model via the string theory
methods. The 3DHl in the cl'itical regime can be assu.I.il-'i;d' to
corr-espond to the fermionic string which s.pans a 2"0 world-sheet.
The 301M also corresponds to theconventtonal-.2 anct.(" Lagrangia
field theories. It can be shown that the scaling dimenstons of
these two and three-dimensional fields are proportional. Tha
constant of proportionality is heuristically identified with
the Hausdorff dimension of the ~IolĀ·ld-sheet. Computercalculatio"
of the Hausdorff dimension and the scaling dtmeos10ns of the 3D
i:onventional field, the results of which artl available in the
literature, enable numerical evaluation of the critical exponent!
m and B of the. Ising model. Thesa agrae well with experimental
results
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Keywords
Three- Dimensionai Ising Model