ISSN:
1572-9613
Keywords:
Bethe-Peierls map
;
Möbius transformation
;
logistic map
;
mean-field percolation
;
McKay-Berker-Kirkpatrick spin-glass
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract The phase diagram of the one-state Potts model on the closed asymmetric Cayley tree with branching ratior=2 is obtained from the Bethe-Peierls map. The route to chaos, via the period doubling cascade, is obtained by considering the antiferromagnetic coupling limit. The connection of the Potts model with the percolation problem is shown by calculating the order parameter, its susceptibility, the internal energy, and the specific heat as well as their asymptotic behavior at the paramagnetic-ferromagnetic critical point. Due to the type of the lattice and to the polynomial character of the map, this is the simplest known example of a McKay-Berker-Kirkpatrick spin-glass.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01026573
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