Zigzag spin chains with antiferromagnetic-ferromagnetic interactions: Transfer-matrix renormalization group study

Abstract

Properties of the zigzag spin chains with various nearest-neighbor and next-nearest-neighbor interactions are studied by making use of the transfer-matrix renormalization group method. Thermodynamic quantities of the systems (temperature dependence of the susceptibility and the specific heat), as well as the field dependence of the magnetization are analyzed numerically with a high accuracy in the thermodynamic limit. The results have been compared with the recent experimental data on Rb2Cu2Mo3O12.

Weakly anisotropic frustrated zigzag spin chain

“…The model with both antiferromagnetic interactions J 1 , J 2 > 0 (AF-AF model) is well studied [2,3,4,5,6,7]. Lately, there has been considerable interest in the study of F-AF model with the ferromagnetic NN and the antiferromagnetic NNN interactions (J 1 < 0, J 2 > 0) [8,9,10,11,12,13,14]. One of the reasons is understanding of intriguing magnetic properties of a novel class of edge-sharing copper oxides which are described by the F-AF model [15,16,17,18,19,20].…”

“…The isotropic case of this model (∆ 1 = ∆ 2 = 1) is intensively studied last years [11,12,21,22,23]. It is known that the ground state of the isotropic version of the model (1) is ferromagnetic at 0 < J < 1/4 and it becomes a singlet incommensurate state for J > 1/4 [24,25].…”

Entanglement and level crossings in frustrated ferromagnetic rings

“…The entanglement between sublattices has been studied for a number of spin chains and lattices, and extrema of S A have been claimed to characterize some quantum phase transitions [14]. Note also that since it is natural to think of the J 1 -J 2 chain as a 'zigzag ladder' (e.g., [19,20,21]), the sublattice entanglement is simply the entanglement between the two legs of such a ladder. In the mesoscopic (finite-size) context that we are interested in, a J 1 -J 2 ring is likely to be implemented as shown in Fig.…”

“…More recently, this model has attracted a fresh surge of theoretical attention [20,32,33,34,35,36,37,38,39], partly due to the appearance of materials whose spin physics is described by this model (see references in [20,32]). Most studies concentrate on finite magnetic fields or finite temperatures and on properties in the thermodynamic limit [20,28,29,30,31,32,33,34,35,36,37,38], or very near the transition point atβ = 4 [27,34,39,40].…”

Numerical study of the frustrated ferromagnetic spin-\frac {1}{2} chain

“…From theoretical point of view, the later model has been subject of many studies [14][15][16][17][18][19][20] . The complete picture of the phases of this model as a function of the frustration parameter α is unclear up to now.…”