2-Spin Systems on Regular Graphs

2017 ◽  
pp. 145-201
Keyword(s):  
Spin Systems ◽  
Regular Graphs

scholarly journals Fast Algorithms for General Spin Systems on Bipartite Expanders

2021 ◽  
Vol 13 (4) ◽  
pp. 1-18
Author(s):  
Andreas Galanis ◽  
Leslie Ann Goldberg ◽  
James Stewart
Keyword(s):  
Partition Function ◽  
Spin System ◽  
Weighted Graph ◽  
Arbitrary Spin ◽  
Spin Assignment ◽  
Spin Systems ◽  
Regular Graphs ◽  
Canonical Class ◽  
Finite Set ◽  
Polymer Models

A spin system is a framework in which the vertices of a graph are assigned spins from a finite set. The interactions between neighbouring spins give rise to weights, so a spin assignment can also be viewed as a weighted graph homomorphism. The problem of approximating the partition function (the aggregate weight of spin assignments) or of sampling from the resulting probability distribution is typically intractable for general graphs. In this work, we consider arbitrary spin systems on bipartite expander Δ-regular graphs, including the canonical class of bipartite random Δ-regular graphs. We develop fast approximate sampling and counting algorithms for general spin systems whenever the degree and the spectral gap of the graph are sufficiently large. Roughly, this guarantees that the spin system is in the so-called low-temperature regime. Our approach generalises the techniques of Jenssen et al. and Chen et al. by showing that typical configurations on bipartite expanders correspond to “bicliques” of the spin system; then, using suitable polymer models, we show how to sample such configurations and approximate the partition function in Õ( n 2 ) time, where n is the size of the graph.

scholarly journals Spin systems on k-regular graphs with complex edge functions

2012 ◽  
Vol 461 ◽  
pp. 2-16 ◽  
Author(s):  
Jin-Yi Cai ◽  
Michael Kowalczyk
Keyword(s):  
Spin Systems ◽  
Regular Graphs

Graphical displays of the motion of spin systems

1996 ◽  
Vol 89 (5) ◽  
pp. 1397-1408 ◽  
Author(s):  
LAWRENCE LOHR
Keyword(s):  
Spin Systems ◽  
Graphical Displays

Dipole magnetic ordering in nuclear spin-spin systems

1975 ◽  
Vol 116 (7) ◽  
pp. 485 ◽  
Author(s):  
V.G. Pokazan'ev ◽  
G.V. Skrotskii ◽  
L.I. Yakub
Keyword(s):  
Nuclear Spin ◽  
Magnetic Ordering ◽  
Spin Systems

21,22-Disubstituted 18α,19βH-Ursane Derivatives with Oxabicyclooctane System in Ring E

1993 ◽  
Vol 58 (1) ◽  
pp. 173-190 ◽  
Author(s):  
Eva Klinotová ◽  
Jiří Klinot ◽  
Václav Křeček ◽  
Miloš Buděšínský ◽  
Bohumil Máca
Keyword(s):  
Spectral Data ◽  
Spin Systems ◽  
Coupling Constants ◽  
Complete Analysis ◽  
Nmr Spectrum ◽  
Proton Proton ◽  
H Nmr ◽  
Proton Coupling ◽  
C Nmr

Reaction of 3β-acetoxy-21,22-dioxo-18α,19βH-ursan-28,20β-olide (IIIa) and 20β,28-epoxy-21,22-dioxo-19α,19βH-ursan-3β-yl acetate (IIIb) with diazomethane afforded derivatives XII-XIV with spiroepoxide group in position 21 or 22, which were further converted into hydroxy derivatives XV and XVII. Ethylene ketals VIII-X were also prepared. In connection with the determination of position and configuration of the functional groups at C(21) and C(22), the 1H and 13C NMR spectral data of the prepared compounds are discussed. Complete analysis of two four-spin systems in the 1H NMR spectrum of bisethylenedioxy derivative Xb led to the proton-proton coupling constants from which the structure with two 1,4-dioxane rings condensed with ring E, and their conformation, was derived.

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