1997/12/12 by Guy B. Standen, Standen, Guy B., David J. Toms +1
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #Superconductivity (cond-mat.supr-con) #Theoretical and Computational Physics #cond-mat.stat-mech #cond-mat.supr-con
paper · pdf · doi:10.48550/arxiv.cond-mat/9712141
22 pages including 11 encapsulated postscript figures
arxiv created 1997/12/12 · openalex publication_date 1997/12/12 · arxiv updated 2009/11/30 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28
The statistical mechanics of a system of non-relativistic charged particles\nin a constant magnetic field is discussed. The spatial dimension D is\narbitrary with D\≥ 3 assumed. Calculations are presented from first\nprinciples using the effective action method. For D\≥ 5 the system has a\nphase transition with a Bose condensate. We show how the effective action\nmethod method deals with in a very natural way with the condensate and study\nit's r ole in the magnetization of the gas. For large values of the magnetic\nfield we show how the magnetized gas in D spatial dimensions behaves like the\nfree Bose gas in (D-2) spatial dimensions. Even though for D=3 the magnetized\ngas does not have a phase transition for any non-zero value of the magnetic\nfield, we show how the specific heat starts to resemble the result for the free\ngas as the magnetic field is reduced. A number of analytical approximations for\nthe magnetization and specific heat are given and compared with numerical\nresults. In this way we are able to study in precise detail how the B\→ 0\nlimit of the magnetized gas is achieved.\n