A String Theory Approach To The Three- Dimensionai Ising Model
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The thre(!"-d"lmctlsional ISing mode"' (3DII~) hilS been Olie tdrnthe unsolved problems in physics. Polyakov hiS sugg0sted ~hltrnIt may be possible to solve this model via the string theoryrnmethods. The 3DHl in the cl'itical regime can be assu.I.il-'i;d' torncorr-espond to the fermionic string which s.pans a 2"0 world-sheet.rnThe 301M also corresponds to theconventtonal-.2 anct.(" Lagrangiarnfield theories. It can be shown that the scaling dimenstons ofrnthese two and three-dimensional fields are proportional. Tharnconstant of proportionality is heuristically identified withrnthe Hausdorff dimension of the ~Iol·ld-sheet. Computercalculatio"rnof the Hausdorff dimension and the scaling dtmeos10ns of the 3Drni:onventional field, the results of which artl available in thernliterature, enable numerical evaluation of the critical exponent!rnm and B of the. Ising model. Thesa agrae well with experimentalrnresults
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