Topic

# Landau theory

About: Landau theory is a(n) research topic. Over the lifetime, 2882 publication(s) have been published within this topic receiving 57078 citation(s).

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TL;DR: In this article, the authors describe how phase transitions occur in practice in practice, and describe the role of models in the process of phase transitions in the Ising Model and the Role of Models in Phase Transition.

Abstract: Introduction * Scaling and Dimensional Analysis * Power Laws in Statistical Physics * Some Important Questions * Historical Development * Exercises How Phase Transitions Occur In Principle * Review of Statistical Mechanics * The Thermodynamic Limit * Phase Boundaries and Phase Transitions * The Role of Models * The Ising Model * Analytic Properties of the Ising Model * Symmetry Properties of the Ising Model * Existence of Phase Transitions * Spontaneous Symmetry Breaking * Ergodicity Breaking * Fluids * Lattice Gases * Equivalence in Statistical Mechanics * Miscellaneous Remarks * Exercises How Phase Transitions Occur In Practice * Ad Hoc Solution Methods * The Transfer Matrix * Phase Transitions * Thermodynamic Properties * Spatial Correlations * Low Temperature Expansion * Mean Field Theory * Exercises Critical Phenomena in Fluids * Thermodynamics * Two-Phase Coexistence * Vicinity of the Critical Point * Van der Waals Equation * Spatial Correlations * Measurement of Critical Exponents * Exercises Landau Theory * Order Parameters * Common Features of Mean Field Theories * Phenomenological Landau Theory * Continuous Phase Transitions * Inhomogeneous Systems * Correlation Functions * Exercises Fluctuations and the Breakdown of Landau Theory * Breakdown of Microscopic Landau Theory * Breakdown of Phenomenological Landau Theory * The Gaussian Approximation * Critical Exponents * Exercises Scaling in Static, Dynamic and Non-Equilibrium Phenomena * The Static-Scaling Hypothesis * Other Forms of the Scaling Hypothesis * Dynamic Critical Phenomena * Scaling in the Approach to Equilibrium * Summary The Renormalisation Group * Block Spins * Basic Ideas of the Renormalisation Group * Fixed Points * Origin of Scaling * RG in Differential Form * RG for the Two Dimensional Ising Model * First Order Transitions and Non-Critical Properties * RG for the Correlation Function * Crossover Phenomena * Correlations to Scaling * Finite Size Scaling Anomalous Dimensions Far From Equilibrium * Introduction * Similarity Solutions * Anomalous Dimensions in Similarity Solutions * Renormalisation * Perturbation Theory for Barenblatts Equation * Fixed Points * Conclusion Continuous Symmetry * Correlation in the Ordered Phase * Kosterlitz-Thouless Transition Critical Phenomena Near Four Dimensions * Basic Idea of the Epsilon Expansion * RG for the Gaussian Model * RG Beyond the Gaussian Approximation * Feyman Diagrams * The RG Recursion Relations * Conclusion

2,087 citations

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TL;DR: In this paper, a review of quantumphase transition from one state to another is provided by adjusting a tuning parameter other than temperature, and their consequences for finite temperature experiments are discussed.

Abstract: Thermal fluctuations induced by increasing temperature can change the state of matter, for example, when water boils to steam. It also is possible to change the state of matter at absolute zero temperature by quantum fluctuations demanded by Heisenberg's uncertainty principle. In this case, the quantumphase transition from one state to another is provided by adjusting a tuning parameter other than temperature. A few characteristic examples of quantumphase transitions are reviewed, and their consequences for finite temperature experiments are discussed.
Keywords:
quantum phase transitions;
broken symmetry;
Landau theory;
Berry phases;
confinement;
quantum criticality;
deconfined criticality;
spin gap;
monopole;
valence bond solid

1,268 citations

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TL;DR: In this paper, a review of various concepts about first-order phase transitions is given, with particular emphasis on metastable states near first order phase transitions, on the'stability limits' of such states (e.g., the spinodal curve of the gas-liquid transition) and on the dynamic mechanisms by which metastable state decay (nucleation and growth of droplets of a new phase).

Abstract: An introductory review of various concepts about first-order phase transitions is given. Rules for classification of phase transitions as second or first order are discussed, as well as exceptions to these rules. Attention is drawn to the rounding of first-order transitions due to finite-size or quenched impurities. Computational methods to calculate phase diagrams for simple model Hamiltonians are also described. Particular emphasis is laid on metastable states near first-order phase transitions, on the 'stability limits' of such states (e.g. the 'spinodal curve' of the gas-liquid transition) and on the dynamic mechanisms by which metastable states decay (nucleation and growth of droplets of a new phase, etc.).

738 citations

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TL;DR: In this paper, Anderson's statement that in the low-temperature limit the usual Kondos-d model evolves toward a fixed point in which the effective exchange coupling of the impurity with the conduction electrons is infinitely strong is taken as granted.

Abstract: We take as granted Anderson's statement that in the low-temperature limit the usual Kondos-d model evolves toward a fixed point in which the effective exchange coupling of the impurity with the conduction electrons is infinitely strong. The low-temperature properties (T«T
K) are then described phenomenologically in the same spirit as the usual Landau theory of Fermi liquids. The specific heat, spin susceptibility, and resistivity are expressed in terms of a small number of numerical parameters. In the strong coupling case the latter may be obtained via perturbation theory; in the opposite weak coupling limit they must be fitted to Wilson's recent numerical results.

670 citations

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16 Dec 1991

527 citations