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
J1<0 between nearest neighbors and a frustrating antiferromagnetic next-nearest-neighbor in-chain coupling
J2>0. We focus on the moderate strength of frustration
J2<∣J1∣/4 such that the in-chain spin-spin correlations are predominantly ferromagnetic. We consider two interchain couplings (ICs) ${J}_{\ensuremath{\perp},y}$ and ${J}_{\ensuremath{\perp},z}$, corresponding to the two axes 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 a quantum nature. The major part of our study is devoted to the finite-temperature properties. We calculate the critical temperature
Tc as a function of the competing exchange couplings ${J}_{2},{J}_{\ensuremath{\perp},y},{J}_{\ensuremath{\perp},z}$. We find that for fixed ICs,
Tc decreases monotonically with increasing frustration
J2, where as ${J}_{2}\ensuremath{\rightarrow}|{J}_{1}|/4$ the
Tc(J2) curve drops down rapidly. To characterize the magnetic ordering below and above
Tc, we calculate the spin-spin correlation functions $\ensuremath{\langle}{\mathbf{S}}_{0}{\mathbf{S}}_{\mathbf{R}}\ensuremath{\rangle}$, the magnetic order parameter
M, the uniform static susceptibility ${\ensuremath{\chi}}_{0}$, as well as the correlation length $\ensuremath{\xi}$. Moreover, we discuss the specific heat
CV and the temperature dependence of the excitation spectrum ${\ensuremath{\omega}}_{\mathbf{q}}$. As ${J}_{2}\ensuremath{\rightarrow}|{J}_{1}|/4$, some unusual frustration-induced features were found, such as an increase of the in-chain spin stiffness (in the case of ferromagnetic ICs) or of the in-chain spin-wave velocity (in the case of antiferromagnetic ICs) with growing temperature.
The ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model with spatially anisotropic couplings on a square lattice are investigated by a spin-rotation-invariant Green's-function approach and by Lanczos diagonalizations on lattices up to 36 sites supplemented by finite-size scaling. We focus on the anisotropy-driven transition from the N\'eel state to a paramagnetic state with antiferromagnetic short-range order and on the spatial dependence of spin correlation functions. Our principal result is that a rather sharp crossover in the magnetic behavior occurs at the coupling ratio ${R}_{0}\ensuremath{\simeq}0.2 {(R=J}_{y}{/J}_{x}).$