Intermediate statistics: addressing the Landau diamagnetism problem

Quantum groups and quantum algebras have received considerable attention in the last decades because they are very useful as mathematical tools of research. Existing proposals for quantum groups have always suggested the idea of deforming a classical object. Motivated by the possibility of anyons in three dimensions ($d=3$), with important consequences to a wide range of fields of physics, in the present work we investigate how the magnetization and other thermodynamic quantities, associated to the Landau diamagnetism problem, depend on the deforming parameter of two models with intermediate statistics: (i) $q$-fermions and (ii) $F$-anyons, and make {\it comparisons between both cases}. In particular, we extend the results from the literature for $q$-fermions by considering {\it second order terms} in the expansion of the grand partition function. Also, we find that for $F$-anyons statistics the magnetization shows a stronger response with respect to magnetic fields compared to magnetization for $q$-fermions statistics. This theoretical outcome may be experimentally verified for instance in superconductors, that are perfect diamagnetic materials with strong magnetic susceptibility, by adjusting impurities or pressure. The latter can be associated to the deforming parameter $q$.