  In the paper, we study the thermodynamic and electromagnetic properties of
the Penson-Kolb (PK) model, i.e., the tight-binding model for fermionic
particles with the pair-hopping interaction $J$. We focus on the case of
repulsive $J$ (i.e., $J<0$), which can stabilize the eta-pairing
superconductivity with Cooper-pair center-of-mass momentum $\vec{q}=\vec{Q}$,
$\vec{Q}=(\pi/a$,$\pi/a$,\ldots). Numerical calculations are performed for
several $d$-dimensional hypercubic lattices: $d=2$ (the square lattice, SQ),
$d=3$ (the simple cubic lattice) and $d=\infty$ hypercubic lattice (for
arbitrary particle concentration $0<n<2$ and temperature $T$). The ground state
$J$ versus $n$ phase diagrams and the crossover to the Bose-Einstein
condensation regime are analyzed and the evolution of the superfluid
characteristics are examined within the (broken symmetry) Hartree-Fock
approximation (HFA). The critical fields, the coherence length, the London
penetration depth, and the Ginzburg ratio are determined at $T=0$ and $T>0$ as
a function of $n$ and pairing strength. The analysis of the effects of the Fock
term on the ground state phase boundaries and on selected PK model
characteristics is performed as well as the influence of the phase fluctuations
on the eta-pairing superconductivity is investigated. Within the
Kosterlitz-Thouless scenario, the critical temperatures $T_{KT} $ are estimated
for $d=2$ SQ lattice and compared with the critical temperature $T_c$ obtained
from HFA. We also determine the temperature $T_m$ at which minimal gap between
two quasiparticle bands vanishes in the eta-phase. Our results for repulsive
$J$ are contrasted with those found earlier for the PK model with attractive
$J$ (i.e., with $J>0$).
