Nearest-Particle Systems

Abstract

Nearest-particle systems are one-dimensional spin systems in which the flip rates depend on η in a certain way which we will now describe. Configurations η ∈ X = {0,1}^Z1 will be given an occupancy interpretation: η(x) = 1 means that there is a particle at x, and η( x) = 0 means that x is vacant. For x ∈ Z¹ and η ∈ X, let l_x (η) and r_x (η) be the distances from x to the nearest particle to the left and right respectively:

$$ \begin{array}{*{20}c} {lx(\eta ) = x - \max \{ y < x:\eta (y) = 1\} ,{\text{ }}and} \\ {rx(\eta ) = \min (y > x:\eta (y) = 1\} - x.} \\ \end{array} $$