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On the use of “small external fields” in the problem of symmetry breakdown in statistical mechanics

✍ Scribed by David Ruelle

Publisher
Elsevier Science
Year
1972
Tongue
English
Weight
503 KB
Volume
69
Category
Article
ISSN
0003-4916

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✦ Synopsis

We study the infinite system equilibrium states in the statistical mechanics of classical lattice gases. We show that breakdown of the translation invariance occurs if and only if the derivative dP(@ + hY)/dX is discontinuous at h = 0 for some Y. In this formula, P is the pressure, @ the translation invariant interaction of the system, and I a "small external field" from a suitable class of nontranslation invariant interactions. In an appendix we show that an Ising ferromagnet in a nonvanishing magnetic field has only one equilibrium state.

📜 SIMILAR VOLUMES

The problem of equivalence in statistica
The problem of equivalence in statistical mechanics of equilibrium
✍ J. Schröter; R. Wegener 📂 Article 📅 1991 🏛 John Wiley and Sons 🌐 English ⚖ 432 KB

## Abstract The physical problem of the equivalence of certain partition function in statistical mechanics leads to the following mathematical problem: Under what conditions is the logarithm of a Laplace–Stieltjes transform of the so‐called microcanonical partition function equal to a Legendre tran