Edge Miracle: Phase Transitions and Critical Phenomena

Author: Yu Lu/Hao Beijing/Chen Xiaosong
Publisher:
Publish Date: 2005-07-01
Features: Phase transitions and critical phenomena are one of the most challenging and unexpectedly rewarding fields in physics. Precise mathematical language elevates physics to an art. Only those who diligently master the mathematical language can eventually appreciate the beauty of this art after deep study. The myriad forms of "water," the question of "whether there are permanent gases?" theories that are correct in spaces with more than four dimensions, and non-equilibrium phase transitions—the order and chaos in nature—0°C ice melting into water, 100°C water boiling into steam, are commonplace phenomena. Think carefully: why do these 1023 water molecules, with their individual structures and interactions unchanged, "collectively" and "unprompted" transition from one phase to another? How does the "new phase" "emerge" and "form" within the "old phase"? This small book guides readers into the bizarre and vibrant "world of phase transitions": from the changes in the three states of matter, ferromagnetism, ferroelectricity, liquid crystal phase transitions, to Bose-Einstein condensation, superfluidity, and superconductivity. The book also extends the concept of equilibrium phase transitions to other systems, including geometric phase transitions and non-equilibrium phase transitions. By introducing phase transitions and critical phenomena, this book elucidates the fundamental concepts of thermodynamics and statistical physics, from the introduction of entropy and statistical partition functions to symmetry breaking, scaling laws, and universality. It also describes the basic theoretical methods for studying phase transition phenomena, including mean-field approximation, scaling analysis, renormalization group, exact solutions of statistical models, and computer numerical simulations. The book also introduces the latest advancements in phase transition research, such as critical phenomena in finite systems and quantum phase transitions. This book serves as a foundational text in theoretical physics, with rich content, engaging narration, and stunning illustrations, making it suitable for readers with a basic understanding of science and engineering at the early university level.