Statistical Mechanics - Physics at Oregon State University

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156 CHAPTER 7. CLASSICAL STATISTICAL MECHANICS. The virial for a classical system is defined by V = thermal average of V is equal to −3NkBT . Problem 8. i dpi ri dt . Show that the Consider the quantity L(t) = i ri(t)pi(t). Show that the thermal average of L(t) is independent of time.
Chapter 8 Mean Field Theory: critical temperature. 8.1 Introduction. When are systems interesting? In the previous chapters we have developed the principles of statistical mechanics. Most of the applications were to simple models. The only important system we discussed in detail was a gas of independent particles. The model we discussed for that system is very important, since a gas is almost always close to ideal. Quantum effects can be explained in this model in a qualitative way. The theoretical model of an ideal gas is also a very good starting point for the treatment of a real gas, as we will see in a next chapter. In this chapter we discuss systems of real interest. By that we mean systems that show a phase transition from one state to another. Real systems, of course, are quite complex, so we need to find a simple model that applies to realistic systems, yet can be approximately solved by analytical means. Therefore, we focus on a theoretical model which applies to many effects encountered in solids. The most important characteristic of a solid is the fact that the atomic positions are fixed, if we ignore the small fluctuations due to phonons. With each atomic position we can associate other degrees of freedom, like spin or atom-type. Solid state physics is concerned with the procedures of obtaining information pertaining to these degrees of freedom, experimentally as well as theoretically. Theoretical models of internal degrees of freedom coupled to fixed lattice sites are called lattice models. These models play an important role in many areas of physics and can be generalized to cases where particles are moving and are not restricted to specific lattice sites. Here we will only discuss the most elementary member of the class of lattice models, the Ising model. We will use 157
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Statistical Mechanics Henri J.F. Ja
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IV CONTENTS 4.3 Gas of poly-atomic
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VI CONTENTS
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VIII INTRODUCTION Introduction. The
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X INTRODUCTION In chapter nine we d
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2 CHAPTER 1. FOUNDATION OF STATISTI
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10 CHAPTER 1. FOUNDATION OF STATIST
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44 CHAPTER 3. VARIABLE NUMBER OF PA
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68 CHAPTER 4. STATISTICS OF INDEPEN
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90 CHAPTER 5. FERMIONS AND BOSONS
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92 CHAPTER 5. FERMIONS AND BOSONS t
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230 APPENDIX A. SOLUTIONS TO SELECT
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Statistical Mechanics - Physics at Oregon State University

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