Oscillations of Observables in 1Dimensional Lattice Systems
Abstract
Using, and extending, striking inequalities by V.V. Ivanov on the downcrossings of monotone functions and ergodic sums, we give universal bounds on the probability of finding oscillations of observables in 1dimensional lattice gases in infinite volume. In particular, we study the finite volume average of the occupation number as one runs through an increasing sequence of boxes of size $2n$ centered at the origin. We show that the probability to see $k$ oscillations of this average between two values $\beta $ and $0<\alpha <\beta $ is bounded by $C R^k$, with $R<1$, where the constants $C$ and $R$ do not depend on any detail of the model, nor on the state one observes, but only on the ratio $\alpha/\beta $.
 Publication:

arXiv eprints
 Pub Date:
 May 1997
 DOI:
 10.48550/arXiv.condmat/9705175
 arXiv:
 arXiv:condmat/9705175
 Bibcode:
 1997cond.mat..5175C
 Keywords:

 Condensed Matter  Statistical Mechanics