There is also a road from Sauk City, known as the river road, which passes Lodde's Mill and Cassell Prairie on the way.
"Baraboo, Dells, and Devil's Lake Region" by H. E. Cole
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While the number of structural fires in the United States continues to decline, firefighter line of duty deaths (LODD) do not exhibit the same rate of proportion decline.
Fire Chief Outlines Changes Following LODD.
Lawsuit Seeks to Stop Demolition of Chicago LODD Site.
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Suppose that h = 0 and that the underlying graph is bipartite; this means that L can be partitioned into two sets Leven and Lodd such that sites in Leven only have edges to sites in Lodd , and vice versa.
The random geometry of equilibrium phases
The hard-core model analogue of introducing an external ﬁeld in the Ising model on Zd is obtained by replacing the single activity parameter λ by two different activities λeven and λodd , one for sites in Leven and the other for sites in Lodd .
The random geometry of equilibrium phases
We need to assume that the underlying lattice L is bipartite, and thus splits off into two parts, Leven and Lodd .
The random geometry of equilibrium phases
If |h| < 2d, there exist two periodic ground states, ηeven and ηodd = −ηeven , where ηeven ≡ 1 on Leven and ηeven ≡ −1 on Lodd . (There are no other periodic ground states, see for example .) The phase transition in this model has been studied in and [129].
The random geometry of equilibrium phases
In the statement above, an inﬁnite n-cluster for a conﬁguration σ is an inﬁnite cluster of the subgraph of Zd obtained by keeping only those edges e ∈ B with (σ(x), σ(y)) ∈ Gn , where x is the endpoint of e in the even sublattice Leven and y ∈ Lodd is the other endpoint of e.
The random geometry of equilibrium phases
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