The book "Modern Theory of Critical Phenomena" by Shang-keng Ma, published in 1976 and republished in 2018, is an introductory text on the modern theory of critical phenomena. It is designed for graduate students and researchers in physical sciences and engineering, requiring only elementary statistical mechanics as a prerequisite. The book covers the fundamental concepts and advanced topics in critical phenomena, focusing on the renormalization group (RG) approach developed by K. G. Wilson in 1971. The first part of the book provides a brief overview of critical phenomena, including definitions of critical points, order parameters, and critical exponents. It also discusses mean field theory and the Gaussian approximation. The second part delves into more advanced topics, such as the scaling hypothesis, fixed points, and the renormalization group in dynamics. Key topics include: - **Introduction to Critical Phenomena**: Definitions and qualitative features of critical behavior. - **Renormalization Group**: Concepts, definitions, and applications. - **Scaling Hypothesis**: Phenomenological hypothesis and scale transformations. - **Fixed Points and Exponents**: Connection to critical exponents. - **Dynamic Critical Phenomena**: Mode-mode coupling, relaxation times, and dynamic scaling. - **Perturbation Expansions**: ε expansion and 1/n expansion. - **Effect of Random Impurities**: Discussion on the impact of impurities on critical behaviors. The book emphasizes the importance of symmetry transformations in understanding complex physical problems and highlights the role of the RG in simplifying the study of critical phenomena. It also addresses the limitations and uncertainties in the field, encouraging readers to explore and contribute to ongoing research.The book "Modern Theory of Critical Phenomena" by Shang-keng Ma, published in 1976 and republished in 2018, is an introductory text on the modern theory of critical phenomena. It is designed for graduate students and researchers in physical sciences and engineering, requiring only elementary statistical mechanics as a prerequisite. The book covers the fundamental concepts and advanced topics in critical phenomena, focusing on the renormalization group (RG) approach developed by K. G. Wilson in 1971. The first part of the book provides a brief overview of critical phenomena, including definitions of critical points, order parameters, and critical exponents. It also discusses mean field theory and the Gaussian approximation. The second part delves into more advanced topics, such as the scaling hypothesis, fixed points, and the renormalization group in dynamics. Key topics include: - **Introduction to Critical Phenomena**: Definitions and qualitative features of critical behavior. - **Renormalization Group**: Concepts, definitions, and applications. - **Scaling Hypothesis**: Phenomenological hypothesis and scale transformations. - **Fixed Points and Exponents**: Connection to critical exponents. - **Dynamic Critical Phenomena**: Mode-mode coupling, relaxation times, and dynamic scaling. - **Perturbation Expansions**: ε expansion and 1/n expansion. - **Effect of Random Impurities**: Discussion on the impact of impurities on critical behaviors. The book emphasizes the importance of symmetry transformations in understanding complex physical problems and highlights the role of the RG in simplifying the study of critical phenomena. It also addresses the limitations and uncertainties in the field, encouraging readers to explore and contribute to ongoing research.