Journal of Statistical Physics

, Volume 76, Issue 5–6, pp 1505–1510 | Cite as

Upper bounds onTc for one-dimensional Ising systems

  • James L. Monroe
Short Communications
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Accepted:

Abstract

We present upper bounds on the critical temperature of one-dimensional Ising models with long-range,l/nα interactions, where 1<α≦2. In particular for the often studied case of α=2 we have an upper bound onTc which is less than theTc found by a number of approximation techniques. Also for the case where α is small, such as α=1.1, we obtain rigorous bounds which are extremely close, within 1.0%, to those found by approximation methods.

Key Words

Ising model long-range interactions critical temperature 
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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • James L. Monroe
    • 1
  1. 1.Department of Physics, Beaver CampusPenn State UniversityMonáca

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