Wavelength-dependent fluctuations in classical paramagnets in a magnetic field. I. Static properties

Abstract

Four functions are introduced to describe the response of classical paramagnets to fluctuations in basic 'mechanical' and 'thermal' wavelength-dependent variables, and the response functions reduce, in the long-wavelength limit, to the specific heats at constant field and magnetization and the isothermal and isentropic susceptibilities. A response function is proportional to the mean square fluctuation in its associated variable, which is analogous to the well known results obtained from the theory of thermodynamic fluctuations in a fluid. The wavelength, temperature and field dependences of the response functions are studied for the one-dimensional classical Heisenberg model, for which exact results can be obtained. Approximate analytic results are derived for the low-temperature inverse correlation lengths and isothermal susceptibilities of ferro- and antiferromagnetically coupled systems in finite applied fields. Particular attention is paid to the behaviour, as a function of field, of an antiferromagnetically coupled model, emphasizing the rather striking features which occur at field strengths typifying a change from antiferromagnetic to ferromagnetic character.