具體描述
內容簡介
Some ten years ago, when completing with J.-B. Zuber a previous text on Quantum Field Theory, the senior author was painfully aware that little mention was made that methods in statistical physics and Euclidean field theory were coming closer and closer, with common tools based on the use of path integrals and the renormalization group giving insights on global structures. It was partly to fill this gap that the present book was undertaken. Alas, over the five years that it took to come to life, both subjects have undergone a new evolution. Disordered media, growth patterns, complex dynamical systems or spin glasses are among the new important topics in statistical mechanics, while superstring theory has turned to the study of extended systems, Kaluza-Klein theories in higher dimensions, anticommuting coordinates ... in an attempt to formulate a unified model including all known interactions. New and sophisticated techniques have invaded statistical physics, ranging from algebraic methods in integrable systems to fractal sets or random surfaces. Powerful computers or special devices provide "experimental" means for a new brand of theoretical physicists. In quantum field theory, applications of differential topology, geometry, Riemannian manifolds, operator theory ... require a deeper background in mathematics and a knowledge of some of its most recent developments. As a result, when surveying what has been included in the present volume in an attempt to uncover the basic unity of these subjects, the authors have the same unsatisfactory feeling of not being able to bring the reader really up to date. It is presumably the fate of such endeavours to always come short of accomplishing their purpose.目錄
Contents of Volume 2Preface
1 From Brownian motion to Euclidean fields
1.1 Brownian motion
1.1.1 Random walks
1.1.2 The sum over paths
1.1.3 The dimension two of Brownian curves
1.2 Euclidean fields
1.2.1 Free fields
1.2.2 Interacting fields and random walks
1.2.3 Self-avoiding walks and the limit n → 0
1.2.4 Comparison with the high temperature expansion
1.2.5 The one-dimensional case
1.A Lattices
Notes
2 Grassmannian integrals and the two-dimensional Ising model
2.1 Grassmannian integrals
2.1.1 Anticommuting variables
2.1.2 Integrals
2.2 The two-dimensional Ising model
2.2.1 Duality
2.2.2 Transfer matrix
2.2.3 Fermionic representation
2.2.4 Free energy
2.2.5 Spontaneous magnetization
2.2.6 Correlation function in the high temperature phase
2.2.7 Surface tension
2.3 Critical continuous theory
2.3.1 Effective action
2.3.2 Correlation functions
2.A Quadratic differences and Painleve equations Notes
3 Spontaneous symmetry breaking, mean field
3.1 Mean field approximation
3.1.1 Dielectric coastant of a polarizable medium
3.1.2 Classical spin model with a finite symmetry group
3.1.3 Continuous symmetry group
3.1.4 The Bethe approximation
3.1.5 Critical exponents
3.2 Lee-Yang zeroes
3.2.1 The Lee-Yang theorem
3.2.2 The one-dimensional case
3.2.3 General properties
3.2.4 Zeroes in the temperature plane
3.3 Large n limit
3.3.1 Saddle point method
3.3.2 Factorization
3.3.3 Coupling to an external field
3.4 Corrections to mean field
3.4.1 Laplace transform Notes
4 Scaling transformations and the XY-model
4.1 Scaling laws. Real space renormalization
4.1.1 Homogeneity and scale invariance
4.1.2 Recurrence relations in real space
4.1.3 Examples and approximations
4.2 The XY-model
4.2.1 High temperature behaviour
4.2.2 Low temperature expansion. Vortices
4.2.3 The Villain action
4.2.4 Correlations
4.2.5 Renormalization flow
4.A Two-dimensional systems with continuous symmetry
4.A.1 Magnetization inequality
4.A.2 Correlation inequality
4.B Phenomenological renormalization Notes
5 Continuous field theory and the renormalization group
5.1 The Lagrangian and dimensional analysis
5.1.1 Introduction
5.1.2 Generating functionals and dimensional analysis
5.2 The perturbative method
5.2.1 Diagrammatic series
5.2.2 Loop expansion
5.2.3 Evaluation of integrals and dimensional continuation
5.2.4 Group theoretical factors
5.2.5 Power counting
5.2.6 Perturbativc renormalization
5.3 The renormalization group
5.3.1 Renormalization flow
5.3.2 Critical exponents
5.3.3 From the Gaussian ultraviolet fixed point to the infrared critical point in dimension less than four
5.3.4 Correlation functions at the critical point
5.3.5 Expansion near the critical point
5.3.6 Scaling laws below the critical temperature
5.4 Corrections to scaling laws
5.4.1 Deviation from the critical point in dimension lower than four
5.4.2 Logarithmic corrections in dimension four
5.4.3 Irrelevant operators
5.5 Numerical results
5.5.1 e-expansion of critical exponents
5.5.2 Equation of state
5.5.3 Amplitude ratios
5.5.4 Three-dimensional results
5.A Multicritical points Notes
6 Lattice gauge fields
6.1 Generalities
6.1.1 Presentation
6.1.2 The continuous limit
6.1.3 Order parameter and Elitzur''s theorem
6.1.4 Duality
6.2 Structure of the phase diagram
6.2.1 Mean field approximation
6.2.2 Corrections to mean field and restoration of gauge invariance
6.2.3 Discrete groups: 1/d expansion
6.2.4 Continuous groups: computation of corrections
6.3 Strong coupling expansions
6.3.1 Convergence
6.3.2 Character expansions
6.3.3 Free energy
6.3.4 String tension and roughening transition
6.3.5 Mass spectrum
6.4 Lattice fermions
6.4.1 The doubling problem
6.4.2 The Nielsen-Ninomiya theorem
6.4.3 Staggered fermions
Notes
Index
前言/序言
用戶評價
這本書的封麵設計簡潔而富有力量，當我第一次看到它時，就立刻被吸引住瞭。那流暢的綫條和深邃的色彩，仿佛預示著一場關於抽象概念和數學工具的宏大探索。我一直在尋找一本能夠將統計力學和場論這兩個看似獨立的領域進行有機整閤的書籍，而《統計場論（第1捲）》似乎正是為此而生。盡管我還沒有開始深入閱讀，但僅從其標題和齣版信息來看，它所承載的學術深度和前沿性就足以讓我充滿期待。我知道，統計場論是理解復雜係統，例如凝聚態物理、粒子物理甚至某些生物係統行為的關鍵。這本書很可能包含瞭從基礎的概率論和統計力學概念，逐步過渡到更高級的量子場論在統計係統中的應用，這對於我目前的學術研究方嚮至關重要。我希望它能提供一種清晰的、循序漸進的講解方式，幫助我理解那些復雜的數學推導和物理直覺。尤其是，我期待書中能夠闡述如何利用場論的語言來描述和分析統計係統的集體行為，例如相變、臨界現象等。這本書的齣現，無疑為我打開瞭一扇新的研究視野。
評分這本書的齣現，對於我這樣一位長期在統計物理領域探索的學者來說，無疑是一個振奮人心的消息。我一直覺得，統計力學雖然強大，但在描述某些復雜係統的湧現行為時，似乎缺少一種更具普適性和幾何直覺的語言。《統計場論（第1捲）》這個書名，立刻引起瞭我的高度關注，它暗示著一種可能性，即利用場論的強大工具來解決統計力學中的難題。我猜想，書中會詳細介紹如何將統計係統的自由能或者分配函數看作一個“場”，然後運用量子場論的手段來研究這個場的性質。我非常期待書中能夠對各種統計場論的經典模型進行深入的解析，比如如何利用路徑積分來計算統計係統的各種物理量，如何通過重整化群來理解臨界現象的普適性。如果書中還能包含一些關於拓撲場論在統計力學中的最新進展，那就更令人激動瞭。這本書的引進，無疑將極大地豐富我們對復雜係統行為的理解。
評分當我看到《統計場論（第1捲）》這本書時，一種強烈的求知欲被點燃瞭。長期以來，我一直在努力理解統計力學和場論是如何在更深層次上相互關聯的。很多時候，我們雖然掌握瞭各自獨立的理論框架，但在麵對一些復雜的、跨尺度的問題時，卻感到力不從心。這本書的名字預示著它可能填補瞭這一空白。我設想，書中會從統計學最基本的概率分布齣發，一步步構建起描述多體係統行為的場論框架。我想象著那些關於格林函數、重整化群、以及對稱性破缺的深刻論述，它們將如何被巧妙地運用到理解統計係統的相變和臨界行為中。我期待著它能提供一套係統的、完整的理論體係，讓我能夠用一種更統一、更強大的工具去分析和預測各種復雜的物理現象。這本書的到來，讓我覺得我的知識體係正在得到一次前所未有的拓展和升華，我對即將開始的閱讀充滿瞭無限的憧憬。
評分當我第一次在書店的架子上看到《統計場論（第1捲）》這本書時，它的名字就吸引瞭我。我一直在尋找一本能夠將統計力學的概念與場論的強大數學工具結閤起來的書，這本書似乎正是為此而設計的。我設想，它會從統計力學的基本原理齣發，逐步引入場論的概念，比如如何用場來描述一個多體係統的狀態，以及如何利用場論的方法來計算係統的熱力學性質。我特彆期待書中能夠對一些經典的統計場論模型進行詳細的講解，例如伊辛模型在統計場論中的應用，以及如何利用重整化群來研究臨界現象。如果書中還能介紹一些更前沿的統計場論技術，那就更好瞭。這本書的齣現，為我提供瞭一個深入學習統計場論的絕佳機會，我迫不及待地想翻開它，開始我的探索之旅。
評分初見《統計場論（第1捲）》，我的腦海中立刻浮現齣那些在學術會議上聽到的激動人心的報告，以及在研究前沿文獻中瞥見的那些抽象而迷人的公式。這本書的名字本身就充滿瞭誘惑力，它承諾將統計學的嚴謹性與場論的普適性相結閤，這對於任何一個醉心於探索物質世界底層規律的物理學傢來說，都是一個無法抗拒的邀請。我預感，這不僅僅是一本教科書，更可能是一部能夠激發靈感的思想之作。它或許會帶領我們穿越微觀世界的量子漲落，進入宏觀世界的集體湧現，用一種全新的、統一的視角去理解那些曾經看似難以解釋的物理現象。我特彆好奇書中是否會對各種統計場論模型進行詳細的介紹和比較，比如伊辛模型、標度律、以及更復雜的量子場論在統計力學中的應用。如果這本書能夠提供豐富的例子和案例研究，那就更妙瞭，能夠幫助我更直觀地把握那些抽象的理論。我把它放在書架上，感到一種莫名的踏實，仿佛它是我學術旅途中一位不可或缺的嚮導。
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