Domain statistics in a finite Ising chain

Details Domain statistics in a finite Ising chain Domain statistics in a finite Ising chain

2006-03-15

arxiv.org/abs/cond-mat/0603417v1

Phys. Rev. E 71, 046137 (2005) (8 pages)

Physics

Condensed Matter

Statistical Mechanics

19 pages

Scientific paper

10.1103/PhysRevE.71.046137

We present a comprehensive study for the statistical properties of random variables that describe the domain structure of a finite Ising chain with nearest-neighbor exchange interactions and free boundary conditions. By use of extensive combinatorics we succeed in obtaining the one-variable probability functions for (i) the number of domain walls, (ii) the number of up domains, and (iii) the number of spins in an up domain. The corresponding averages and variances of these probability distributions are calculated and the limiting case of an infinite chain is considered. Analyzing the averages and the transition time between differing chain states at low temperatures, we also introduce a criterion of the ferromagnetic-like behavior of a finite Ising chain. The results can be used to characterize magnetism in monatomic metal wires and atomic-scale memory devices.

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