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Re: finding a symplectic recursion fixed point

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112039] Re: finding a symplectic recursion fixed point
  • From: Roger Bagula <roger.bagula at gmail.com>
  • Date: Thu, 26 Aug 2010 06:48:22 -0400 (EDT)
  • References: <i5065f$gha$1@smc.vnet.net>

It might help to see the original Migdal-Kadanoff and the fixed point:
T = Exp[b0]*Exp[{{b1, -b1}, {-b1, b1}}];
T1 = Exp[b01]*Exp[{{b11, -b11}, {-b11, b11}}];
B = T.T - T1;
Flatten[Table[B[[i, j]] == 0, {i, 2}, {j, 2}]]
Solve[Flatten[Table[B[[i, j]] == 0, {i, 1}, {j, 2}]], {b01, b11}]
Solve[Flatten[Table[B[[i, j]] == 0, {i, 2}, {j, 1}]], {b01, b11}]
b1=Log[1+Sqrt[2]]/2
Source:
http://books.google.com/books?id=mcCyB3ewyeMC&pg=PA117&lpg=PA117&dq=migdal-kadanoff+recursion&source=bl&ots=WJMD1Oau3D&sig=3NdwgMgxMdNjgeic3Xj0c2x0fWc&hl=en&ei=DEV1TPigNofWtQP6l5ygDQ&sa=X&oi=book_result&ct=result&resnum=8&ved=0CDQQ6AEwBzgK#v=onepage&q=migdal-kadanoff%20recursion&f=false


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