Universal low-temperature properties of frustrated classical spin chain near the ferromagnet-helimagnet transition point

Abstract

The thermodynamics of the classical frustrated spin chain near the transition point between the ferromagnetic and the helical phases is studied. The calculation of the partition and spin correlation functions at low temperature limit is reduced to the quantum mechanical problem of a particle in potential well. It is shown that the thermodynamic quantities are universal functions of the temperature normalized by the chiral domain wall energy. The obtained behavior of the static structure factor indicates that the short-range helical-type correlations existing at low temperatures on the helical side of the transition point disappear at some critical temperature, defining the Lifshitz point. It is also shown that the low-temperature susceptibility in the helical phase near the transition point has a maximum at some temperature. Such behavior is in agreement with that observed in several materials described by the quantum s = 1/2 version of this model. * Electronic address: dmitriev@deom.chph.ras.ru

Chirality Transitions in Frustrated Ferromagnetic Spin Chains: A Link with the Gradient Theory of Phase Transitions

“…Thus, near the ferromagnet-helimagnet transition point, the energy C α coincides with the energy E dw ∝ (4 − α) 3/2 for the excitation of a chiral domain wall separating two domains of opposite chirality, which is a well-known universal low-temperature property of frustrated classical spin chains (see, e.g., Dmitriev and Krivnov [14]).…”

Chirality transitions in frustrated S2-valued spin systems

“…As we have seen, this restriction leads to a positive limit energy when changing the chirality. However, this energy is independent of the distance between two chirality vectors in contrast to the results conjectured in [14]. To obtain such a dependence we propose another model, where we penalize the distance of u from the set M k with an additional energy term.…”

“…As discussed in the previous section, it is not possible to energetically detect chirality transitions by using as energy H n , that is the scaled NN and NNN frustrated spin chain model as in [13]. Nevertheless, transitions with non trivial energy may appear if we modify the functional H n by adding what we call either a hard or a soft penalization term.…”

Chirality transitions in frustrated ferromagnetic chains

“…The two terms in the energy compete: the first is ferromagnetic and favors the alignment of neighboring spins while the second is antiferromagnetic and favors antipodal next-to-nearest neighboring spins (see [9] for additional informations regarding the model and its quantum mechanical analogue). Similar studies as the one considered in this contribution can be found in [1], [2], [3] for spin variables having a discrete symmetry (e.g., the Ising system where u ∈ {±1}).…”