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Tiling problems and undecidability in the cluster variation method

Journal of Statistical Physics, ISSN: 0022-4715, Vol: 50, Issue: 3-4, Page: 689-714
1988
  • 12
    Citations
  • 0
    Usage
  • 8
    Captures
  • 0
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    12
    • Citation Indexes
      12
  • Captures
    8

Article Description

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. © 1988 Plenum Publishing Corporation.

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