Abstract
In this note we prove a correlation inequality for local variables of a Gibbs field based on the connectivity in a random cluster representation of the non overlap configuration distribution of two independent copies of the field. As a consequence, we show that absence of a particular type of percolation (of Machta–Newman–Stein blue bonds) implies uniqueness of Gibbs distribution in EA Spin Glasses. In dimension two this could constitute a step towards a proof that the critical temperature is zero.
Original language | English (US) |
---|---|
Pages (from-to) | 249-267 |
Number of pages | 19 |
Journal | Journal of Statistical Physics |
Volume | 173 |
Issue number | 2 |
DOIs | |
State | Published - Oct 1 2018 |
Keywords
- Correlation inequalities
- Disagreement percolation
- Gibbs fields
- Random cluster representation
- Spin glasses
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics