251From Frictional Instabilities to Friction-Induced Self-Organization
Ri
o
(8.73)
where
is a uniform potential eld and
is the position of the lattice
with respect to the reference frame.
Monte Carlo simulations of Potts models have traditionally used local
algorithms such as that of Metropolis (Graner and Glazer 1992). A lattice
site (i,j) is chosen at random and a new trial spin is also chosen at random
from one of its surroundings to test local boundary energy minimization
(Figure8.21). The probability P of accepting such a reassignment is (Graner
and Glazer 1992)
P
H
HkT/
=
≤
≤
−
(8.74)
where ΔH is the difference between total energy before and after the spin
reassignment, T is the magnitude of uctuations, and k