Reduction of spin glasses applied to
the Migdal-Kadanoff hierarchical lattice |
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Authors: | Email author" target="_blank">S?BoettcherEmail author |
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Institution: | (1) Physics Department, Emory University, Atlanta, Georgia 30322, USA |
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Abstract: | A reduction procedure to obtain ground states of spin
glasses on sparse graphs is developed and tested on the
hierarchical lattice associated with the Migdal-Kadanoff
approximation for low-dimensional lattices. While more generally
applicable, these rules here lead to a complete reduction of the
lattice. The stiffness exponent governing the scaling of the
defect energy E with system
size L, (E) ~L
y, is obtained as
y
3 = 0.25546(3) by reducing the equivalent
of lattices up to L =
2100 in d = 3, and as y
4 = 0.76382(4) for up to
L =
235 in d = 4. The reduction rules allow the
exact determination of the ground state energy, entropy, and
also provide an approximation to the overlap distribution. With
these methods, some well-know and some new features of diluted
hierarchical lattices are calculated. |
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Keywords: | 05 50 +q Lattice theory and statistics (Ising Potts etc ) 75 10 Nr Spin-glass and other random models 02 60 Pn Numerical optimization |
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