Coarse-grained models of stripe forming systems: Phase diagrams, anomalies, and scaling hypothesis

Abstract

Two coarse-grained models which capture some universal characteristics of stripe forming systems are studied. At high temperatures, the structure factors of both models attain their maxima on a circle in reciprocal space, as a consequence of generic isotropic competing interactions. Although this is known to lead to some universal properties, we show that the phase diagrams have important differences, which are a consequence of the particular k dependence of the fluctuation spectrum in each model. The phase diagrams are computed in a mean field approximation and also after inclusion of small fluctuations, which are shown to modify drastically the mean field behavior. Observables like the modulation length and magnetization profiles are computed for the whole temperature range accessible to both models and some important differences in behavior are observed. A stripe compression modulus is computed, showing an anomalous behavior with temperature as recently reported in related models. Also, a recently proposed scaling hypothesis for modulated systems is tested and found to be valid for both models studied.

Interplay of spin waves and vortices in the two-dimensional XY model at small vortex-core energy

“…[40] using the effective couplings discussed in Eqs. (23) and (24). This analysis slightly improves the accuracy of the predicted critical temperatures especially at high μ values, as shown with the blue diamonds in Fig.…”

“…It is worth noting that the RG analysis performed using the effective couplings Eqs. (23) and (24) estimated using the coefficients in Table I greatly improves the accuracy of the two-step approach in the μ = 0 case, with respect to the traditional KT initial condition μ v = π 2 2 J eff . As the coupling μ increases, the RG results increasingly deviate from the MC estimates, in agreement with the expectations of larger corrections to the Coulomb gas approximation.…”

“…Theoretically, the BKT scaling is the key to understand the universal features of a wide range of natural phenomena ranging from DNA tangling in biology to pattern formation in complex systems [22][23][24]. The hallmark of such a scaling is the expected discontinuous jump of the phase stiffness J s from a finite value J s (T BKT ) at the BKT temperature T BKT to zero right above it.…”

On the mechanism behind the inverse melting in systems with competing interactions

“…(5) At this point a relation between arctanh(φ( x, t)) and φ( x, t) is necessary, and different approximations could be used 32 . In the present work, we begin by using the standard mean-field approach, neglecting all fluctuations in the local order parameter: arctanh(φ( x, t)) ∼ = arctanh( φ( x) ).…”

“…Additionally, the values of the critical fields as a function of the reduced temperature are very close. Considering that the strict mean field approach has been used more often in previous works 29,32 , in what follows the overall presented analysis have been obtained within this approximation.…”