ABSTRACT
This chapter is devoted exclusively to systems in equilibrium. First it considers the quantum statistics of systems like the Bose or Fermi gas, then it considers lattice spin systems and the nonideal classical gas. Quantum statistics is Euclidean field theory on a finite time interval with the additional condition that the fields be periodic. Functional integrals in statistics differ from the integrals of Euclidean field theory only by the finiteness of the range of integration over time in the action functional and the periodicity requirements on the fields. The classical Heisenberg model differs from the Ising model in that with each lattice site is associated a classical d-dimensional spin vector s of unit length. The chapter also discusses the case of a gas with many-body forces which is interesting mainly because it leads to a diagrammatic technique which lies outside ordinary graph theory.
