Stable solution of the simplest spin model for inverse freezing

Inverse transitions and disappearance of the λ-line in the asymmetric random-field Ising and Blume-Capel models

We report on reentrance in the random-field Ising and Blume-Capel models, induced by an asymmetric bimodal random-field distribution. The conventional continuous line of transitions between the paramagnetic and ferromagnetic phases, the λ-line, is wiped away by the asymmetry. The phase diagram, then, consists of only first-order transition lines that always end at ordered critical points. We find that, while for symmetric random-field distributions there is no reentrance, the asymmetry in the random-field results in a range of temperatures for which magnetization shows reentrance. While this does not give rise to an inverse transition in the Ising model, for the Blume-Capel model, however, there is a line of first-order inverse phase transitions that ends at an inverse-ordered critical point. We show that the location of the inverse transitions can be inferred from the ground-state phase diagram of the model.

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

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.

Impact-induced gelation in aqueous methylcellulose solutions

Inverse-freezing materials were known to solidify when heated – now a new stimulus is shown to induce this transition within microseconds’ timescales: mechanical impacts.

Effect of geometrical frustration on inverse freezing

The interplay between geometrical frustration (GF) and inverse freezing (IF) is studied within a cluster approach. The model considers first-neighbor (J_{1}) and second-neighbor (J_{2}) intracluster antiferromagnetic interactions between Ising spins on a checkerboard lattice and long-range disordered couplings (J) among clusters. We obtain phase diagrams of temperature versus J_{1}/J in two cases: the absence of J_{2} interaction and the isotropic limit J_{2}=J_{1}, where GF takes place. An IF reentrant transition from the spin-glass (SG) to paramagnetic (PM) phase is found for a certain range of J_{1}/J in both cases. The J_{1} interaction leads to a SG state with high entropy at the same time that can introduce a low-entropy PM phase. In addition, it is observed that the cluster size plays an important role. The GF increases the PM phase entropy, but larger clusters can give an entropic advantage for the SG phase that favors IF. Therefore, our results suggest that disordered systems with antiferromagnetic clusters can exhibit an IF transition even in the presence of GF.

Dynamical arrest with zero complexity: The unusual behavior of the spherical Blume-Emery-Griffiths disordered model

The short- and long-time dynamics of model systems undergoing a glass transition with apparent inversion of Kauzmann and dynamical arrest glass transition lines is investigated. These models belong to the class of the spherical mean-field approximation of a spin-1 model with p-body quenched disordered interaction, with p>2, termed spherical Blume-Emery-Griffiths models. Depending on temperature and chemical potential the system is found in a paramagnetic or in a glassy phase and the transition between these phases can be of a different nature. In specific regions of the phase diagram coexistence of low-density and high-density paramagnets can occur, as well as the coexistence of spin-glass and paramagnetic phases. The exact static solution for the glassy phase is known to be obtained by the one-step replica symmetry breaking ansatz. Different scenarios arise for both the dynamic and the thermodynamic transitions. These include: (i) the usual random first-order transition (Kauzmann-like) for mean-field glasses preceded by a dynamic transition, (ii) a thermodynamic first-order transition with phase coexistence and latent heat, and (iii) a regime of apparent inversion of static transition line and dynamic transition lines, the latter defined as a nonzero complexity line. The latter inversion, though, turns out to be preceded by a dynamical arrest line at higher temperature. Crossover between different regimes is analyzed by solving mode-coupling-theory equations near the boundaries of paramagnetic solutions and the relationship with the underlying statics is discussed.

Inverse transitions in a spin-glass model on a scale-free network

In this paper, we will investigate critical phenomena by considering a model spin glass on scale-free networks. For this purpose, we consider the Ghatak-Sherrington (GS) model, a spin-1 spin-glass model with a crystal field, instead of the usual Ising-type model. Scale-free networks on which the GS model is placed are constructed from the static model, in which the number of vertices is fixed from the beginning. On the basis of the replica-symmetric solution, we obtain the analytical solutions, i.e., free energy and order parameters, and we derive the various phase diagrams consisting of the paramagnetic, ferromagnetic, and spin-glass phases as functions of temperature T, the degree exponent λ, the mean degree K, and the fraction of the ferromagnetic interactions ρ. Since the present model is based on the GS model, which considers the three states (S = 0, ± 1), the S = 0 state plays a crucial role in the λ-dependent critical behavior: glass transition temperature T(g) has a finite value, even when 2 < λ < 3. In addition, when the crystal field becomes nonzero, the present model clearly exhibits three types of inverse transitions, which occur when an ordered phase is more entropic than a disordered one.

Spin-1 Hopfield model under a random field

The goal of the present work is to investigate the role of trivial disorder and nontrivial disorder in the three-state Hopfield model under a Gaussian random field. In order to control the nontrivial disorder, the Hebb interaction is used. This provides a way to control the system frustration by means of the parameter a=p/N, varying from trivial randomness to a highly frustrated regime, in the thermodynamic limit. We performed the thermodynamic analysis using the one-step replica-symmetry-breaking mean field theory to obtain the order parameters and phase diagrams for several strengths of a, the anisotropy constant, and the random field.

Spin-glass splitting in the quantum Ghatak-Sherrington model

We propose an expanded spin-glass model, called the quantum Ghatak-Sherrington model, which considers spin-1 quantum spin operators in a crystal field and in a transverse field. The analytic solutions and phase diagrams of this model are obtained by using the one-step replica symmetry-breaking ansatz under the static approximation. Our results represent the splitting within one spin-glass (SG) phase depending on the values of crystal and transverse fields. The two separated SG phases, characterized by a density of filled states, show certain differences in their shapes and phase boundaries. Such SG splitting becomes more distinctive when the degeneracy of the empty states of spins is larger than one of their filled states.

Inverse melting and inverse freezing in a three-state spin-glass model with finite connectivity

The phase diagrams of the three-state Ghatak-Sherrington spin-glass (or random Blume-Capel) model are obtained in mean-field theory with replica symmetry in order to study the effects of a ferromagnetic bias and finite random connectivity in which each spin is connected to a finite number of other spins. It is shown that inverse melting from a ferromagnetic to a low-temperature paramagnetic phase may appear for small but finite disorder and that inverse freezing appears for large disorder. There can also be a continuous inverse ferromagnetic to spin-glass transition.

Inverse freezing in a cluster Ising spin-glass model with antiferromagnetic interactions

Inverse freezing is analyzed in a cluster spin-glass (SG) model that considers infinite-range disordered interactions between magnetic moments of different clusters (intercluster interaction) and short-range antiferromagnetic coupling J(1) between Ising spins of the same cluster (intracluster interaction). The intercluster disorder J is treated within a mean-field theory by using a framework of one-step replica symmetry breaking. The effective model obtained by this treatment is computed by means of an exact diagonalization method. With the results we build phase diagrams of temperature T/J versus J(1)/J for several sizes of clusters n(s) (number of spins in the cluster). The phase diagrams show a second-order transition from the paramagnetic phase to the SG order at the freezing temperature T(f) when J(1)/J is small. The increase in J(1)/J can then destroy the SG phase. It decreases T(f)/J and introduces a first-order transition. In addition, inverse freezing can arise at a certain range of J(1)/J and large enough n(s). Therefore, the nontrivial frustration generated by disorder and short-range antiferromagnetic coupling can introduce inverse freezing spontaneously.

Liquid-crystalline nanoparticles: Hybrid design and mesophase structures

Liquid-crystalline nanoparticles represent an exciting class of new materials for a variety of potential applications. By combining supramolecular ordering with the fluid properties of the liquid-crystalline state, these materials offer the possibility to organise nanoparticles into addressable 2-D and 3-D arrangements exhibiting high processability and self-healing properties. Herein, we review the developments in the field of discrete thermotropic liquid-crystalline nanoparticle hybrids, with special emphasis on the relationship between the nanoparticle morphology and the nature of the organic ligand coating and their resulting phase behaviour. Mechanisms proposed to explain the supramolecular organisation of the mesogens within the liquid-crystalline phases are discussed.

Inverse freezing in the Ghatak-Sherrington model with a random field

The present work studies the Ghatak-Sherrington (GS) model in the presence of a magnetic random field (RF). Previous results obtained from the GS model without a RF suggest that disorder and frustration are the key ingredients to produce spontaneous inverse freezing (IF). However, in this model, the effects of disorder and frustration always appear combined. In that sense, the introduction of RF allows us to study the IF under the effects of a disorder which is not a source of frustration. The problem is solved within the one step replica symmetry approximation. The results show that the first order transition between the spin glass and the paramagnetic phases, which is related to the IF for a certain range of crystal field D, is gradually suppressed when the RF is increased.

Simplest model to study reentrance in physical systems

We numerically investigate the necessary ingredients for reentrant behavior in the phase diagram of physical systems. Studies on the possibly simplest model that exhibits reentrance, the two-dimensional random-bond Ising model, show that reentrant behavior is generic whenever frustration is present in the model. For both discrete and continuous disorder distributions, the phase diagram in the disorder-temperature plane is found to be reentrant, where for some disorder strengths a paramagnetic phase exists at both high and low temperatures, but an ordered ferromagnetic phase exists for intermediate temperatures.

Phase transitions in the three-state Ising spin-glass model with finite connectivity

The statistical mechanics of a two-state Ising spin-glass model with finite random connectivity, in which each site is connected to a finite number of other sites, is extended in this work within the replica technique to study the phase transitions in the three-state Ghatak-Sherrington (or random Blume-Capel) model of a spin glass with a crystal-field term. The replica symmetry ansatz for the order function is expressed in terms of a two-dimensional effective-field distribution, which is determined numerically by means of a population dynamics procedure. Phase diagrams are obtained exhibiting phase boundaries that have a reentrance with both a continuous and a genuine first-order transition with a discontinuity in the entropy. This may be seen as "inverse freezing," which has been studied extensively lately, as a process either with or without exchange of latent heat.

Thermodynamic first order transition and inverse freezing in a 3D spin glass

We present a numerical study of the random Blume-Capel model in three dimensions. The phase diagram is characterized by spin-glass-paramagnet phase transitions of both first and second order in the thermodynamic sense. Numerical simulations are performed using the exchange Monte Carlo algorithm, providing clear evidence for inverse freezing. The main features at criticality and in the phase coexistence region are investigated. We are not privy to other 3D short-range systems with quenched disorder undergoing inverse freezing.

Phase diagram of a solution undergoing inverse melting

The phase diagram of alpha -cyclodextrin/water/4-methylpyridine solutions, a system undergoing inverse melting, has been studied by differential scanning calorimetry, rheological methods, and x-ray diffraction. Two different fluid phases separated by a solid region have been observed in the high alpha -cyclodextrin concentration range (c > or =150 mg/ml) . Decreasing c , the temperature interval where the solid phase exists decreases and eventually disappears, and a first-order phase transition is observed between the two different fluid phases.

Shear-thickening and entropy-driven reentrance

We discuss a generic mechanism for shear thickening analogous to entropy-driven phase reentrance. We implement it in the context of nonrelaxational mean-field glassy systems: although very simple, the microscopic models we study present a dynamical phase diagram with second- and first-order stirring-induced jamming transitions leading to intermittency, metastability, and phase coexistence as seen in some experiments. The jammed state is fragile with respect to change in the stirring direction. Our approach provides a direct derivation of a mode-coupling theory of shear thickening.