We study the isotropic Heisenberg chain with nearest and next-nearest neighbor interactions. The ground state phase diagram is constructed in dependence on the additional interactions and an external magnetic field. The thermodynamics is studied by use of finite sets of nonlinear integral equations resulting from integrability. The equations are solved numerically and analytically in suitable limiting cases. We find second and first order transition lines. The exponents of the low-temperature asymptotics at the phase transitions are determined.
We study the isotropic Heisenberg chain with nearest and next-nearest neighbor interactions. The ground state phase diagram is constructed in dependence on the additional interactions and an external magnetic field. The thermodynamics is studied by the use of finite sets of nonlinear integral equations resulting from integrability. The equations are solved numerically and analytically in suitable limiting cases. We find second- and first-order transition lines. The exponents of the low-temperature asymptotics at the phase transitions are determined.
We study quantum spin models with nearest- and next-nearest-neighbor exchange interactions by means of exact solutions. Depending on the representation, the models can also be viewed as spin ladders with interchain couplings and with ring biquadratic spin-spin interactions. The ground-state phase diagram is constructed as a function of the next-nearest-neighbor couplings and an external magnetic field. Several quantum phase transitions in the ground state, including the possibility of a first-order quantum phase transition, governed by the external magnetic field, are predicted. The low-energy conformal behavior of the low-lying excitations is studied in the commensurate and incommensurate phases. Finally, the properties of the models at finite temperature are studied exactly. A finite set of nonlinear integral equations determining the thermodynamic potential at arbitrary temperature and external magnetic field is derived and solved in several important cases. The results for the magnetic susceptibility and the Sommerfeld coefficient of the specific heat are presented.
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.