Abstract
Qualitatively new features arise for the case when the system has infinitely many degrees of freedom, namely spontaneous symmetry breaking and phase transition. These concepts are of great interest in solid state physics, dealing with many-particle systems with about 1023 particles. In this chapter, starting with the concept of the order parameter and the basics of the Landau theory, we proceed to a discussion of the Goldstone mode and the absence of order in low-dimensional systems. In the second half of the chapter we will focus on phase transitions, where the topological defects play important roles and it is not easy to find the order parameters, as is the case for the Kosterlitz—Thouless transition, and the confinement in gauge theories on a lattice.
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