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Acta Phys. Polon.

ON THE STATE OF A FERMI-SYSTEM WITH CORRELATION OF PAIRS OF PARTICLES WITH PARALLEL SPINS. II. THERMODYNAMICS

Zygmunt M. Galasiewicz

Published Jan 1, 1960• 0 citations
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Abstract

The thermodynamics of the anomalous state of a Fermi-system (in which the correlation of pairs of particles with parallel spins is taken into account) were investigated. The transition temperature T/sub c/ to the anomalous state was found, as well as the temperature dependence the specific heat for T approx equal i O and T approx equal T/sub c/. For T = T/sub c/ the specific heat has a jump. In addition, formulas for the paramagnetic susceptibilities for T approx equal O and T approx equal T/sub c/ were obtained. (auth)

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Progress of Theoretical Physics•Apr 1, 1954•0 citations
The thermodynamics of the anomalous state of a Fermi-system (in which the correlation of pairs of particles with parallel spins is taken into account) were investigated. The transition temperature T/sub c/ to the anomalous state was found, as well as the temperature dependence the specific heat for T approx equal i O and T approx equal T/sub c/. For T = T/sub c/ the specific heat has a jump. In addition, formulas for the paramagnetic susceptibilities for T approx equal O and T approx equal T/sub c/ were obtained. (auth)
S>The solution of a compensation equation of dangerous graphs, for a system of interacting Fermi-particles, as an odd function of wave vectors is investigated. It is shown that this solution leads to the anomalous state, the energy of which is smaller than the energy of the normal state. The energy difference is equal to the binding energy of the pairs of fermions with parallel spin-moments. This anomalous state can exist in the presence of attractive Coulomb interactions. The elementary excitations are separated from the ground state by a gap the width of which depends on the direction of the wave vector. For the direction perpendicular to the spin direction, energy gap is zero and therefore the state cannot be superconducting. The binding energy of the pairs and the width of the energy gap are of the same order as in the theory based on the creation of pairs with antiparallel spin-moments, where in the expansion of the interaction term in spherical harmonics, the first coefficient is more than three times greater than the zero coefficient. In the absence of the magnetic field the total spin of a system is zero. In the presence of the magnetic field the total spinmore » differs from zero. The paramagnetic susceptibility is calculated. (auth)« less
High-temperature expansions for the specific heat and susceptibility of the strongly correlated Hubbard model are compared with corresponding quantities for spinless free fermions and free spins. It is found numerically that, when the temperature is high, the ratio of the specific heat of the strongly correlated Hubbard model to that of spinless free fermions approaches a particle-density-dependent constant. For fixed temperature, the susceptibility of the Hubbard model is less (greater) than that of free spins when the particle density is below (above) a certain threshold density of approximately 0.7. The ratio of the susceptibilities for the two systems, however, appears to be finite for any value of the particle density. Given that the free spin system does not have a ferromagnetic state at any finite temperature, it is concluded that the strongly correlated Hubbard model does not have a finite phase transition temperature. This conclusion is consistent with recent high-temperature expansion studies.
For the ideal Fermi gas that fills a quantum well confined by two parallel planes, there are calculated the thermodynamic characteristics in general form for arbitrary temperatures, namely: the thermodynamic potential, energy, entropy, equations of state, heat capacities and compressibilities. The distance between planes is considered as an additional thermodynamic variable. Owing to the anisotropy, the pressure of the Fermi gas along and transverse to the planes is different, so that the system is characterized by two equations of state and a set of different heat capacities. Limiting cases of low and high temperatures are considered. The temperature dependencies of the entropy and heat capacities at low temperatures remain linear, just as in the volume case, and their dependencies on the chemical potential and density undergo jumps at the beginning of the filling of new discrete levels. It is shown that the behavior of thermodynamic quantities with the distance between plates can be either oscillating or monotonic, depending on what quantity is assumed to be fixed: the volume or surface density. For high temperatures the corrections to thermodynamic quantities are obtained, which are proportional to the ratio of the thermal de Broglie wavelength to the distance between planes.
The thermodynamic functions of a Fermi gas with spin population imbalance are studied in the temperature-asymmetry plane. The low temperature domain is characterized by anomalous enhancement of the entropy and the specific heat above their values in the unpaired state, decrease of the gap and eventual unpairing phase transition as the temperature is lowered. The unpairing phase transition induces a second jump in the specific heat, which can be measured in calorimetric experiments. While the superfluid is unstable against a supercurrent carrying state, it may sustain a metastable state if cooled adiabatically down from the stable high-temperature domain. In the latter domain the temperature dependence of the gap and related functions is analogous to the predictions of the BCS theory.
The spin susceptibility χ(T)χ(T)χ(T) of strongly correlated Fermi systems is investigated in the density region where Fermi-liquid theory fails. We attribute this failure to a specific quantum phase transition associated with a rearrangement of the Landau state at low temperatures TTT, retaining the assumption that the Landau quasiparticle picture survives in a generic sense. Taking into account the resulting modification of the quasiparticle istribution function, the spin susceptibility χ(T)χ(T)χ(T) is shown to contain a Curie-Weiss component χCW(T)∼(T−ΘW)−1χ_{\rm CW}(T)\sim (T-Θ_{\rm W})^{-1}χCW​(T)∼(T−ΘW​)−1, with the Weiss temperature ΘWΘ_{\rm W}ΘW​ vanishing at the critical density for the transition.