ISSN:
1572-9613
Keywords:
Ising model with long-range interactions
;
Sierpiński-gasket lattice
;
correlation functions
;
chaos
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract A class of multispin correlation functions of an Ising model with ferromagnetic nearest neighbor interactionsK and constant (distance-independent) long-range interactionsQ 1=Q,l=1,2,..., on the Sierpiński-gasket lattice is considered. Using an exact method for calculating thermodynamic functions of hierarchically constructed Ising systems, it is shown that, for a set of values ofQ and for almost all values ofK, someM k-spin correlation functions, whereM k=3 k +3 withk=1,2,...,n andn=1,2,... being the order of lattice construction, change chaotically asn, k, and therebyM k increase to infinity. Accordingly, in the thermodynamic limit, these correlation functions prove to be nonanalytic for appropriate values ofQ andK. SinceM k-point correlation functions withk being finite, i.e., correlation functions involving finite numbers of spins, remain analytic asn tends to infinity, there is a smooth crossover between analytic properties of correlation functions of the two types.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02179804
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