Unified theories on the magnetism and on the critical Casimir force

Abstract : We will pedagogically explore Pauli paramagnetism, Landau diamagnetism and de Haas-van Alphen effect in a single framework for an ideal gas of electrons, and unify these three effects for all temperatures and fields [1]. Then we will switch to a technical work on the critical Casimir force on the He-4 film [2]. That the confinement of critical fluctuations around the lambda point gives rise to a (critical) Casimir force, which causes the thinning of the film, was investigated experimentally by Garcia and Chan [PRL 83, 1187 (1999)] and by Ganshin et al [PRL 97, 075301 (2006)]. We will present a unified theory for the critical Casimir force below and above of the lambda point in a single frame work. Our result goes beyond the previous mean field result [Zandi et al, PRE 76, 030601(R) (2007)], and compares favourably with the numerical simulation [Hucht, PRL 99, 185301 (2007)] and with the experimental data.