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1.

図書

図書
Joaquín Marro, Ronald Dickman
出版情報: Cambridge : Cambridge University Press, 1999  xv, 327 p. ; 25-26 cm
シリーズ名: Collection Aléa-Saclay : monographs and texts in statistical physics
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2.

図書

図書
Geoffrey Grimmett
出版情報: Berlin : Springer, c2006  xiii, 377 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 333
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目次情報: 続きを見る
Random-Cluster Measures / 1:
Introduction / 1.1:
Random-cluster model / 1.2:
Ising and Potts models / 1.3:
Random-cluster and Ising/Potts models coupled / 1.4:
The limit as q [down arrow] 0 / 1.5:
Basic notation / 1.6:
Monotonic Measures / 2:
Stochastic ordering of measures / 2.1:
Positive association / 2.2:
Influence for monotonic measures / 2.3:
Sharp thresholds for increasing events / 2.4:
Exponential steepness / 2.5:
Fundamental Properties / 3:
Conditional probabilities / 3.1:
Differential formulae and sharp thresholds / 3.2:
Comparison inequalities / 3.4:
Partition functions / 3.5:
Domination by the Ising model / 3.7:
Series and parallel laws / 3.8:
Negative association / 3.9:
Infinite-Volume Measures / 4:
Infinite graphs / 4.1:
Boundary conditions / 4.2:
Infinite-volume weak limits / 4.3:
Infinite-volume random-cluster measures / 4.4:
Uniqueness via convexity of pressure / 4.5:
Potts and random-cluster models on infinite graphs / 4.6:
Phase Transition / 5:
The critical point / 5.1:
Percolation probabilities / 5.2:
Uniqueness of random-cluster measures / 5.3:
The subcritical phase / 5.4:
Exponential decay of radius / 5.5:
Exponential decay of volume / 5.6:
The supercritical phase and the Wulff crystal / 5.7:
Uniqueness when q < 1 / 5.8:
In Two Dimensions / 6:
Planar duality / 6.1:
The value of the critical point / 6.2:
First-order phase transition / 6.3:
General lattices in two dimensions / 6.5:
Square, triangular, and hexagonal lattices / 6.6:
Stochastic Lowner evolutions / 6.7:
Duality in Higher Dimensions / 7:
Surfaces and plaquettes / 7.1:
Basic properties of surfaces / 7.2:
A contour representation / 7.3:
Polymer models / 7.4:
Discontinuous phase transition for large q / 7.5:
Dobrushin interfaces / 7.6:
Probabilistic and geometric preliminaries / 7.7:
The law of the interface / 7.8:
Geometry of interfaces / 7.9:
Exponential bounds for group probabilities / 7.10:
Localization of interface / 7.11:
Dynamics of Random-Cluster Models / 8:
Time-evolution of the random-cluster model / 8.1:
Glauber dynamics / 8.2:
Gibbs sampler / 8.3:
Coupling from the past / 8.4:
Swendsen-Wang dynamics / 8.5:
Coupled dynamics on a finite graph / 8.6:
Box dynamics with boundary conditions / 8.7:
Coupled dynamics on the infinite lattice / 8.8:
Simultaneous uniqueness / 8.9:
Flows in Poisson Graphs / 9:
Potts models and flows / 9.1:
Flows in the Ising model / 9.2:
Exponential decay for the Ising model / 9.3:
The Ising model in four and more dimensions / 9.4:
On Other Graphs / 10:
Mean-field theory / 10.1:
On complete graphs / 10.2:
Main results for the complete graph / 10.3:
The fundamental proposition / 10.4:
The size of the largest component / 10.5:
Proofs of main results for complete graphs / 10.6:
The nature of the singularity / 10.7:
Large deviations / 10.8:
On a tree / 10.9:
The critical point for a tree / 10.10:
(Non-)uniqueness of measures on trees / 10.11:
On non-amenable graphs / 10.12:
Graphical Methods for Spin Systems / 11:
Random-cluster representations / 11.1:
The Potts model / 11.2:
The Ashkin-Teller model / 11.3:
The disordered Potts ferromagnet / 11.4:
The Edwards-Anderson spin-glass model / 11.5:
The Widom-Rowlinson lattice gas / 11.6:
The Origins of FK(G) / Appendix:
List of Notation
References
Index
Random-Cluster Measures / 1:
Introduction / 1.1:
Random-cluster model / 1.2:
3.

図書

図書
edited by Henryk Arodz, Jacek Dziarmaga and Wojciech Hubert Zurek
出版情報: Dordrecht : Kluwer Academic, c2003  x, 404 p. ; 25 cm
シリーズ名: NATO science series ; Series II, Mathematics, physics, and chemistry ; 127
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目次情報: 続きを見る
Preface
Symmetry Breaking and Defects / T.W.B. Kibble
Liquid 4He and Its Superfluidity / O.J. Griffiths ; P.C. Hendry ; P.V.E. McClintock ; H.A. Nichol
The Role of Topological Defects in Cosmology / M. Sakellariadou
Cosmic Defects and Particle Physics Constraints / A.C. Davis
Introduction to the Modern Theory of Phase Transitions / J. Sznajd
Defects in Liquid Crystals: Surface and Interfacial Anchoring Effects / O.D. Lavrentovich
Scaling Laws for Fluxon Formation in Annular Josephson Tunnel Junctions / R. Monaco ; R.J. Rivers
Nonholonomic Field Theory of Vortices and Defect and their Phase Transitions / H. Kleinert
Vortices and Flat Directions: the Uses of Bogomolnyi Bounds / A. Achucarro
Evolution of Local Vortices and Interfaces / H. Arodz
Non-Equilibrium Mott Transition in a Lattice of Bose-Einstein Condensates / J. Dziarmaga ; A. Smerzi ; W.H. Zurek ; A.. Bishop
Spontaneous Breakdown of Chiral Symmetry in QCD / M.A. Nowak
Domain Wall Solutions / T. Vachaspati
Phenomenology of Effective Gravity / G.E. Volovik
Preface
Symmetry Breaking and Defects / T.W.B. Kibble
Liquid 4He and Its Superfluidity / O.J. Griffiths ; P.C. Hendry ; P.V.E. McClintock ; H.A. Nichol
4.

図書

図書
volume editors, H.Z. Cummins, A.P. Levanyuk
出版情報: Amsterdam ; New York : North-Holland , New York, N.Y. : Sole distributors for the USA and Canada, Elsevier Science Pub. Co., 1983  xvii, 666 p. ; 25 cm
シリーズ名: Modern problems in condensed matter sciences ; v. 5
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5.

図書

図書
E. Schöll
出版情報: Berlin ; Tokyo : Springer-Verlag, c1987  xi, 313 p. ; 25 cm
シリーズ名: Springer series in synergetics ; v. 35
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6.

図書

図書
A.D. Bruce and R.A. Cowley
出版情報: London : Taylor and Francis, 1981  326 p. ; 26 cm
シリーズ名: Taylor and Francis monographs on physics
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7.

図書

図書
S.W. Koch
出版情報: Berlin ; New York : Springer-Verlag, 1984  148 p. ; 24 cm
シリーズ名: Lecture notes in physics ; 207
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8.

図書

図書
Jürgen Hafner
出版情報: Berlin ; Tokyo : Springer-Verlag, c1987  xi, 404 p. ; 24 cm
シリーズ名: Springer series in solid-state sciences ; 70
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9.

図書

図書
I.R. Yukhnovskii ; translated from the Russian by A.Y. Saban & S.N. Voitiuk
出版情報: Singapore : World Scientific, c1987  xi, 327 p. ; 22 cm
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10.

図書

図書
Robert Brout
出版情報: New York ; Amsterdam : W.A. Benjamin, 1965  xiii, 202 p. ; 24 cm
シリーズ名: Frontiers in physics
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