## Thermodynamics of Crystalline StatesThermodynamics is a well-established discipline of physics for properties of matter in thermal equilibrium with the surroundings. Applying to crystals, however, the laws encounter undefined properties of crystal lattice, which therefore need to be determined for a clear and well-defined description of crystalline states. Thermodynamics of Crystalline States explores the roles played by order variables and dynamic lattices in crystals in a wholly new way.The book begins by clarifying basic concepts for stable crystals. Next, binary phase transitions are discussed to study collective motion of order variables, as described mostly as classical phenomena. New to this edition is the examination of magnetic crystals, where magnetic symmetry is essential for magnetic phase transitions. The multi-electron system is also discussed theoretically, as a quantum-mechanical example, for superconductivity in metallic crystals. Throughout the book, the role played by the lattice is emphasized and studied in-depth. Thermodynamics of Crystalline States is an introductory treatise and textbook on mesoscopic phenomena in solid states, constituting a basic subject in condensed matter physics. While this book serves as a guide for advanced students in physics and material science, it can also be useful as a reference for all professionals in related fields. Minoru Fujimoto is author of Physics of Classical Electromagnetism (Springer, 2007) and The Physics of Structural Phase Transitions (Springer, 2005). |

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### Contents

1 | |

11 | |

Order Variables and the Adiabatic Potential | 33 |

MeanField Theories of Binary Ordering | 55 |

Pseudospin Clusters | 67 |

Critical Fluctuations | 83 |

Pseudospin Correlations | 96 |

Soliton Theory of LongRange Order | 109 |

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adiabatic potential amplitude anomalies antiferromagnetic applied ﬁeld assume binary Brillouin Brillouin zone characterized classical vectors cluster components condensates consider constant Cooper pair correlation energy critical temperature crystal space curve deﬁned density determined diffraction discussed displacements domains eigenvalue electrons elliptic functions equation equilibrium experimental expressed ferroelectric ferromagnetic ﬁnite ﬁrst ﬂuctuations ﬂux frequency Fujimoto Gibbs function Gibbs potential Hamiltonian hence hyperﬁne inelastic scatterings integral interactions inversion ions Landau lattice point lattice sites magnetic crystals magnetic resonance mean-ﬁeld Meissner effect mesoscopic modiﬁed modulated motion neutron nonlinear normal observed obtain Ohm law order variables paramagnetic particles perovskites perturbed phase transition phonon Phys pinning propagation pseudospin quantum Quantum mechanically reﬂection relation represents respectively shown in Fig signiﬁed soft mode speciﬁc heat speciﬁed spectra spin spin—spin Springer Science+Business Media structure sufﬁciently superconducting symmetry temperature dependent term theory thermal Thermodynamics of Crystalline timescale transverse TSCC wave wavefunction wavevector write written