  The thermodynamics of coupled frustrated ferromagnetic chains is studied
within a spin-rotation-invariant Green's function approach. We consider an
isotropic Heisenberg spin-half system with a ferromagnetic in-chain coupling
$J_1<0$ between nearest neighbors and a frustrating antiferromagnetic
next-nearest neighbor in-chain coupling $J_2>0$. We focus on moderate strength
of frustration $J_2 < |J_1|/4$ such that the in-chain spin-spin correlations
are predominantly ferromagnetic. We consider two inter-chain couplings (ICs)
$J_{\perp,y}$ and $J_{\perp,z}$, corresponding to the two axis perpendicular to
the chain, where ferromagnetic as well as antiferromagnetic ICs are taken into
account. We discuss the influence of frustration on the ground-state properties
for antiferromagnetic ICs, where the ground state is of quantum nature. The
major part of our study is devoted to the finite-temperature properties. We
calculate the critical temperature $T_{c}$ as a function of the competing
exchange couplings $J_{2},J_{\perp,y}, J_{\perp,z}$. We find that for fixed ICs
$T_c$ monotonically decreases with increasing frustration $J_2$, where as $J_2
\to |J_1|/4$ the $T_c(J_2)$-curve drops down rapidly. To characterize the
magnetic ordering below and above $T_c$ we calculate the spin-spin correlation
functions $\langle {\bf S}_0 {\bf S}_{\bf R} \rangle$, the magnetic order
parameter $M$, the uniform static susceptibility $\chi_0$ as well as the
correlation length $\xi$. Moreover, we discuss the specific heat $C_V$ and the
temperature dependence of the excitation spectrum $\omega_{\mathbf{q}}$. As
$J_2 \to |J_1|/4$ some unusual frustration-induced features were found, such as
an increase of the in-chain spin stiffness (in case of ferromagnetic ICs) or of
the in-chain spin-wave velocity (in case of antiferromagnetic ICs) with growing
temperature.

Strongly Correlated Electrons;Statistical Mechanics