Statistical Mechanics and Critical Phenomena: A Brief Overview
S. B. Santra, Purusattam Ray
The basic concepts of statistical mechanics and its application to many-body systems, phase transitions and critical phenomena will be discussed briefly in this chapter. We will be using these ideas frequently in the subsequent lectures. Statistical mechanics describes the thermodynamic behaviour of macroscopic systems from the laws which govern the behaviour of the constituent elements at the microscopic level. The microscopic elements can be atoms, molecules, dipole moments or magnetic moments, etc. A macroscopic system is generally composed of a large number of these elements (of the order of Avogadro number N A ≈ 6.022 × 1023 per mole). Each element may have a large number of internal degrees of freedom associated with different types of motion such as translation, rotation, vibration etc. The constituent elements may interact with the external field applied to the system. There can also be very complex interaction among the constituent elements. The macroscopic properties of a system in the thermodynamic limit is thus determined by the properties of the constituent molecules, their interaction with external field as well as interaction among themselves. For a system of N elements, volume V and density ρ, the thermodynamic limit is defined as lim N → ∞, lim V → ∞ keeping ρ = N/V finite. In this limit, the extensive properties of the system become directly proportional to the size of the system (N or V), while the intensive properties become independent of the size of the system.
Texts and readings in physical sciences•Jan 1, 2011•2 citations