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

Abstract

The competition between a short range attractive interaction and a nonlocal repulsive interaction promote the appearance of modulated phases. In this work we present the microscopic mechanisms leading to the emergence of inverse transitions in such systems by considering a thorough mean-field analysis of a variety of minimal models with different competing interactions. We identify the specific connections between the characteristic energy of the homogeneous and modulated phases and the observed reentrant behaviors in the phase diagram. In particular, we find that reentrance is appreciable when the characteristic energy cost of the homogeneous and modulated phases are comparable to each other, and for systems in which the local order parameter is limited. In the asymptotic limit of high energy cost of the homogeneous phase we observe that the degree of reentrance decreases exponentially with the ratio of the characteristic energy cost of homogeneous and modulated phases. These mean-field results are confronted with Langevin simulations of an effective coarse grained model, confirming the expected extension of the reentrance in the phase diagram. These results shed new light on many systems undergoing inverse melting transitions by qualitatively improving the understanding of the interplay of entropy and energy around the inverse melting points.

Topological phase diagrams of the frustrated Ising ferromagnet

“…Following standard procedures the mean field free energy of the system in the continuum limit is given by 26,29…”

“…Finally we choose the units of energy as the quantity Â(k 0 )/k 2 0 , which leads to the dimensionless free energy functional 26,29…”

“…where prime symbols have been omitted to simplify the notation. This kind of mean field free energy have been extensively used as a starting point to construct the phase diagram of systems with competing interactions by looking at the local structure of the order parameter 26 . However, when the phases need to be distinguished by its symmetries, the desired phase diagram should contain information about the translational and rotational order of the different textures the magnetic system develops.…”

“…Another intriguing issue is the effect produced on the topological phases due to the presence of reentrance in the phase diagrams. Systems like the dipolar ferromagnet can present strong reentrances in the H-T plane, depending on the relative strength of the dipolar and the ferromagnetic interactions 26 . For systems with weak enough repulsive interaction the H-T phase diagram develops an inverse melting in a certain range of the external field.…”

Understanding Reentrance in Frustrated Magnets: the Case of the Er$_2$Sn$_2$O$_7$ Pyrochlore

“…temperature, field, pressure, stoichiometry) is continuously varied. Reentrance has been found in spin glasses [17,18], liquid mixtures [19,20], protein thermodynamics [21], liquid crystals [22,23], bilayer graphene [24], superconductors [25], modulated phases [26,27] and even in black hole thermodynamics [28]. Despite its ubiquity, reentrance is typically unexpected and its explanation in terms of entropic contributions to the free-energy from the underlying microscopic degrees of freedom is usually subtle.…”