By Roger Zelazny
The bestselling writer of the Amber sequence creates a pleasant and dramatic interval delusion populated through conversing canine and characters from well known legend. Accompanying and amplifying the textual content are a chain of 31 full-page illustrations via one of many masters of unusual and bad art.
Originally released in 1993.
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Extra info for A Night in the Lonesome October
74) Such a λ is known as a critical exponent. The calculation of such exponents for a given model is the main goal of many works in this ﬁeld. Finally, let us remark that for the model described by (2) with hl = h = 0 and with the single-spin measure possessing the Lee–Yang property, χ < ∞ for all temperatures. This fact was proven in Ref. 71. 6. Uniqueness of Gibbs States for the Ising Model In this subsection we prove that the set of Gibbs states Gβ of the ferromagnetic Ising model with a homogeneous external ﬁeld h is unique at all temperatures and all dimensions of the lattice if h = 0.
In fact, if σ = σ , then one ﬁnds l ∈ Zd such that σl = σl . The function f (σ) = σl takes diﬀerent values on such σ, σ . , two speciﬁc elements of Ω. Recall that for the Ising model, all spins take values ±1, thus the set Ω consists of vectors σ = (σl )l∈Zd , σl = ±1. We set ξ+ = (σl )l∈Zd , with all σl = 1 and ξ− = (σl )l∈Zd , with all σl = −1. Let L be a sequence of boxes Λ deﬁned by (1). The following lemma plays a key role in the proof of our uniqueness theorem. Lemma 35: Suppose that for any l ∈ Zd and for a sequence of boxes L, each of which contains this l, the convergence σl νβ,∆ (·|ξ+ ) − σl νβ,∆ (·|ξ− ) →0 as Λ → Zd , (76) holds.
By (28), P (β) ≥ 0. If P (β) > 0, there exists a periodic nonergodic Gibbs state, which contradicts |Gβ | = 1 since if Gβ is a singleton, its unique element has to be ergodic. , a phase transition. On the other hand, by (18), χ = lim χΛ = lim Λ→Zd Λ→Zd 1 |Λ| σl σl l,l ∈Λ (p) νβ,Λ , (73) 30 Order, Disorder, and Criticality is the inﬁnite-volume susceptibility if the above order parameter P (β) is −1 . , above the Curie temperature TC = βC ture is deﬁned as the supremum of the values of β −1 for which P (β) > 0.
A Night in the Lonesome October by Roger Zelazny