ISSN:
1572-9613
Keywords:
Classical lattice system
;
variational principle
;
cluster variation method
;
tiling problem
;
undecidability
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract In cluster approximations for lattice systems the thermodynamic behavior of the infinite system is inferred from that of a relatively small, finite subsystem (cluster), approximations being made for the influence of the surrounding system. In this context we study, for translation-invariant classical lattice systems, the conditions under which a state for a cluster admits an extension to a global translation-invariant state. This extension problem is related to undecidable tiling problems. The implication is that restrictions of global translation-invariant states cannot be characterized purely locally in general. This means that there is an unavoidable element of uncertainty in the application of a cluster approximation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01026496
Permalink
