14 Result(s)
within
Chapter
Silvio R. A. Salinas
English
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Chapter
The Ising Model
Most of the experiments in the neighborhood of critical points indicate that critical exponents assume the same universal values, far from the predictions of the “classical theories” (as represented by Landau’...
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Chapter
Statistical Description of a Physical System
The mechanico-statistical analysis of a physical system in equilibrium comprises the following steps: (i) The specification of the microscopic states of the system (which form a set called statistical ensemble); ...
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Chapter
Microcanonical Ensemble
According to the fundamental postulate of statistical mechanics, the accessible microscopic states of a closed system in equilibrium are equally probable. The number of microscopic states of a thermodynamic fluid...
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Chapter
Free Bosons: Bose—Einstein Condensation; Photon Gas
The thermodynamic properties of an ideal gas of bosons can be obtained from the grand partition function
10.1 $$ln\** (T,V,\mu... -
Chapter
Phase Transitions and Critical Phenomena: Classical Theories
Phase transitions and critical phenomena are usual events associated with an enormous variety of physical systems (simple fluids and mixtures of fluids, magnetic materials, metallic alloys, ferroelectric mater...
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Chapter
Nonequilibrium phenomena: II. Stochastic Methods
Instead of trying to present a sketch of the theory of Markovian stochastic processes, which is certainly beyond the scope of this text, we discuss some examples of the application of stochastic methods to analyz...
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Chapter
Introduction to Statistical Methods
We have chosen the problem of the random walk in one dimension to introduce some concepts and techniques of the theory of probabilities. We use this problem to analyze the main features of binomial and Gaussia...
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Chapter
Overview of Classical Thermodynamics
Thermodynamics is the branch of physics that organizes in a systematic way the empirical laws referring to the thermal behavior of macroscopic matter. In contrast to statistical mechanics, it does not require ...
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Chapter
Canonical Ensemble
As in the formalism of thermodynamics, in which alternative representations may be more convenient to use depending on the circumstances, in statistical mechanics we also use other ensembles, besides the micro...
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Chapter
The Grand Canonical and Pressure Ensembles
The canonical ensemble describes a thermodynamic system in contact with a heat reservoir, at a fixed temperature. The canonical partition function of a pure fluid depends on temperature, volume, and number of ...
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Chapter
The Ideal Fermi Gas
Given the volume, the temperature, and the chemical potential, the grand partition function for free fermions may be written in the form
9.1 ... -
Chapter
Phonons and Magnons
We now discuss some additional examples of Bose systems of interest in condensed matter physics. Phonons are quasi-particles produced by the quantization of the elastic vibrations of a crystalline lattice. Mag...
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Chapter
Nonequilibrium Phenomena: I. Kinetic Methods
In the previous chapters of this book we have always referred to phenomena in macroscopic equilibrium, which can be treated and well understood by the formalism of Gibbs ensembles. In this chapter, we revisit ...
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Chapter
Scaling Theories and the Renormalization Group
It is too strong to assume that the free energy of a model system in the critical region can be expanded as a power series of the order parameter. The divergent specific heat of the Onsager exact solution for ...
