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 frustrated ferromagnetic spin-
1∕2 Heisenberg chain is studied by means of a low-energy field theory as well as the density-matrix renormalization group and exact diagonalization methods. First, we study the ground-state phase diagram in a magnetic field and find an ``even-odd'' (EO) phase characterized by bound pairs of magnons in the region of two weakly coupled antiferromagnetic chains. A jump in the magnetization curves signals a first-order transition at the boundary of the EO phase, but otherwise the curves are smooth. Second, we discuss thermodynamic properties at zero field, where we confirm a double-peak structure in the specific heat for moderate frustrating next-nearest-neighbor interactions.
The Ising linear chain with nearest-neighbor interactions of strength J s and infinite long-range ferromagnetic exponential interactions of strength J l was solved exactly in the presence of the external field. The spontaneous magnetization and the susceptibility are obtained. The transition temperature depends on J s and J l . For J s >0, the model shows the second order phase transion. The specific heat shows both a broad peak and a sharp peak. The value of sharp peak of the specific heat depends on J s and J l . For J s <0, the properties of the transition agree with those of Nagle model with long-range equivalent-neighbor ferromagnetic interactions. The exact free energy and the long-range order of our model are identical with those of the variational theory of a quasi-one-dimensional model.
Thermodynamic properties of antiferromagnetic spin chain with various AFM nearest-neighbor and FM next-nearest-neighbor exchange interactions are studied using functional integral method in J 1 – J 2 Heisenberg model. Besides, the excitation spectrum of the system is also given. The results show that the system has two distinct excitations with no energy gap from the ground state for any permissible values of J 1 and J 2 without single-ion anisotropy. Changing the exchange parameters influences on the thermodynamic properties and the excitation spectra of the system.