Thermodynamic and magnetic properties of nonrelativistic "para-Fermi gas"

Abstract

The equation of state, the magnetic moment, as well as a Curie-type law for the susceptibility parameter of a system of particles of spin 1/2 in the presence of an external magnetic field are calculated assuming that these particles obey generalized statistics. Here one assumes that the occupation number of an energy state can take the values 0, 1, 2, ..., 1 and no more, where I is an integer greater than unity. This is a direct consequence of the generalized method of field quantization originally due to Green. Exact expressions for the thermodynamic and magnetic properties due to the generalized nature of the statistics are given, and the characteristic departures of the present results from those of the Fermi-Dirac case are pointed out. Our results are useful for investigating the thermodynamic state and spontaneous magnetization of the highly compressed state of matter, presumably of quarks, obtained in a star in gravitational collapse. The quarks are assumed to obey generalized F e m i statistics known in the literature as para-Fermi statistics.

Thermodynamic Bethe ansatz for generalized extensive statistics

“…where h µ (t) = f ′′ (t)/(µf (t)) + (1 − µ)/t 2 . For any f (t) satisfying ( 7) and x obeying (10) we have h µ (x) > 0 due to the Hadamard theorem [18,19]. From (11) we obtain the entropy density s(µ) for a given value of µ lim…”

“…From the definition of µ it is clear that 0 ≤ µ ≤ d for f (t) of the type I and 0 ≤ µ ≤ ∞ for the other types. Formally this follows from equation (10) which shows that µ varies from µ(x = 0) to µ(x = R). Moreover, µ(x) is a strictly increasing function because ∂ x µ = xµh µ (x) > 0 for x > 0.…”

“…More precisely, s(µ) may have one root at the interval µ(1) < µ ≤ µ(R). Indeed, for f (t) of the type I we derive from (10) and (12) that…”

“…where each x a (θ) satisfies (10) and hence it is a function of ρ r a (θ)/ρ a (θ). The subscript of f a means that different species may have different single-state partition functions.…”

“…Many authors discussed thermodynamic properties of an ideal gas obeying the Gentile or parafermi statistics [6,10,11]. In the present paper we will study the thermodynamic limit of one-dimensional relativistic integrable field models governed by a Gentile-like statistics.…”