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1.

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:
2.

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
3.

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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4.

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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5.

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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6.

図書

図書
Minoru Fujimoto
出版情報: New York : Springer, c1997  xi, 247 p. ; 24 cm
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目次情報: 続きを見る
Thermodynamic Principles and the Landau Theory of Phase Transitions
Order-Disorder Statistics, Short-Range Correlations and the Mean-Field Approximation
Collective Pseudospins in Displacive Phase Transitions and the Born-Huang Theory
Soft Modes, Pseudospin Condensates and Lattice Anharmonicity in the Critical Region
Dynamics of Collective Pseudospins and Long-Range Order
Diffuse X-Ray Diffraction and Neutron Inelastic Scattering from Modulated Crystals
Light Scattering and Dielectric Studies on Structural Phase Transitions
The Spin-Hamiltonian and Magnetic Resonance Spectroscopy
Magnetic Resonance Sampling and Nuclear Relaxation Studies on Modulated Crystals
Structural Phase Transitions in Miscellaneous Systems
Epilogue
Thermodynamic Principles and the Landau Theory of Phase Transitions
Order-Disorder Statistics, Short-Range Correlations and the Mean-Field Approximation
Collective Pseudospins in Displacive Phase Transitions and the Born-Huang Theory
7.

図書

図書
Yuli M. Ivanchenko, Alexander A. Lisyansky
出版情報: New York : Springer-Verlag, c1995  xv, 390 p. ; 24 cm
シリーズ名: Graduate texts in contemporary physics
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8.

図書

図書
edited by Nino Russo and Dennis R. Salahub
出版情報: Dordrecht : Kluwer Academic Pub., c1996  xiv, 552 p. ; 25 cm
シリーズ名: NATO ASI series ; Series C . Mathematical and physical sciences ; v. 474
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9.

図書

図書
by Ya.G. Sinai ; [translated by J. Fritz ... et al.]
出版情報: Oxford ; New York : Pergamon Press, 1982  viii, 153 p. ; 25 cm
シリーズ名: International series in natural philosophy ; v. 108
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10.

図書

図書
by A.Z. Patashinskiĭ and V.L. Pokrovskiĭ ; translated and edited by P. J. Shepherd
出版情報: Oxford ; New York : Pergamon Press, 1979  x, 321 p. ; 26 cm
シリーズ名: International series in natural philosophy ; v. 98
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