Reentrant Phase Diagram Research Articles

Freezing and reentrant melting of hard disks in a one-dimensional potential: Predictions based on a pressure-balance equation

We investigate theoretically the freezing behavior of a two-dimensional system of hard disks on a one-dimensional external potential (typically called laser-induced freezing). As shown by earlier theoretical and numerical studies, one observes freezing of the modulated liquid upon increase of the substrate potential amplitude, and reentrant melting back into the modulated liquid when the substrate potential amplitude is increased even further. The purpose of our present work is to calculate the freezing and reentrant melting phase diagram based on information from the bulk system. To this end, we employ an integrated pressure-balance equation derived from density functional theory [Phys. Rev. E 101, 012609 (2020)2470-004510.1103/PhysRevE.101.012609]. Furthermore, we define a measure to quantify the influence of registration effects that qualitatively explain reentrant melting. Despite severe approximations, the calculated phase diagram shows good agreement with the known phase diagram obtained by Monte Carlo simulations.

Statistical field theory and effective action method for scalar active matter

We employ Statistical Field Theory techniques for coarse-graining the steady-state properties of Active Ornstein-Uhlenbeck particles. The computation is carried on in the framework of the Unified Colored Noise approximation that allows an effective equilibrium picture. We thus develop a mean-field theory that allows to describe in a unified framework the phenomenology of scalar Active Matter. In particular, we are able to describe through spontaneous symmetry breaking mechanism two peculiar features of Active Systems that are (i) The accumulation of active particles at the boundaries of a confining container, and (ii) Motility-Induced Phase Separation (MIPS). \textcolor{black}{We develop a mean-field theory for steric interacting active particles undergoing to MIPS and for Active Lennard-Jones (ALJ) fluids.} \textcolor{black}{Within this framework}, we discuss the universality class of MIPS and ALJ \textcolor{black}{showing that it falls into Ising universality class.} We \textcolor{black}{thus} compute analytically the critical line $T_c(\tau)$ for both models. In the case of MIPS, $T_c(\tau)$ gives rise to a reentrant phase diagram compatible with an inverse transition from liquid to gas as the strength of the noise decreases. \textcolor{black}{However, in the case of particles interacting through anisotropic potentials, } the field theory acquires a $\varphi^3$ term that, \textcolor{black}{in general, cannot be canceled performing the expansion around the critical point.} In this case, the \textcolor{black}{Ising} critical point might \textcolor{black}{be replaced} by a first-order phase transition \textcolor{black}{region}.

Reentrant Phase Diagram of Yb_{2}Ti_{2}O_{7} in a ⟨111⟩ Magnetic Field.

We present a magnetic phase diagram of rare-earth pyrochlore Yb_{2}Ti_{2}O_{7} in a ⟨111⟩ magnetic field. Using heat capacity, magnetization, and neutron scattering data, we show an unusual field dependence of a first-order phase boundary, wherein a small applied field increases the ordering temperature. The zero-field ground state has ferromagnetic domains, while the spins polarize along ⟨111⟩ above 0.65T. A classical MonteCarlo analysis of published Hamiltonians does account for the critical field in the low T limit. However, this analysis fails to account for the large bulge in the reentrant phase diagram, suggesting that either long-range interactions or quantum fluctuations govern low field properties.

Non-classical phase diagram for virus bacterial coevolution mediated by clustered regularly interspaced short palindromic repeats.

CRISPR is a newly discovered prokaryotic immune system. Bacteria and archaea with this system incorporate genetic material from invading viruses into their genomes, providing protection against future infection by similar viruses. The condition for coexistence of prokaryots and viruses is an interesting problem in evolutionary biology. In this work, we show an intriguing phase diagram of the virus extinction probability, which is more complex than that of the classical predator-prey model. As the CRISPR incorporates genetic material, viruses are under pressure to evolve to escape recognition by CRISPR. When bacteria have a small rate of deleting spacers, a new parameter region in which bacteria and viruses can coexist arises, and it leads to a more complex coexistence patten for bacteria and viruses. For example, when the virus mutation rate is low, the virus extinction probability changes non-montonically with the bacterial exposure rate. The virus and bacteria coevolution not only alters the virus extinction probability, but also changes the bacterial population structure. Additionally, we show that recombination is a successful strategy for viruses to escape from CRISPR recognition when viruses have multiple proto-spacers, providing support for a recombination-mediated escape mechanism suggested experimentally. Finally, we suggest that the re-entrant phase diagram, in which phages can progress through three phases of extinction and two phases of abundance at low spacer deletion rates as a function of exposure rate to bacteria, is an experimentally testable phenomenon.

Comparing the influence of distinct kinds of temporal disorder in a low-dimensional absorbing transition model.

Recently it was stated that temporal disorder constitutes a relevant perturbation in absorbing phase transitions for all dimensions. However, its effect on systems other than the standard contact process (CP), its competition with other ingredients (e.g., particle diffusion), and other kinds of disorder (besides the standard types) are unknown. In order to shed some light on the above-mentioned points, we investigate a variant of the usual CP, namely, the triplet annihilation model, in which the competition between triplet annihilation and single particle diffusion leads to an unusual phase diagram behavior, with reentrant shape and endless activity for sufficiently large diffusion rates. Two kinds of time-dependent disorder have been considered. In the former, it is introduced in the creation-annihilation parameters (as commonly considered in recent studies), whereas in the latter, the diffusion rate D is allowed to be time dependent. In all cases, the disorder follows a uniform distribution with fixed mean and width σ. Two values of σ have been considered in order to exemplify the regime of "weaker" and "stronger" temporal disorder strengths. Our results show that in the former approach, the disorder suppresses the reentrant phase diagram with a critical behavior deviating from the directed percolation (DP) universality class in the regime of low diffusion rates, while they strongly suggest that the DP class is recovered for larger hopping rates. An opposite scenario is found in the latter disorder approach, with a substantial increase of reentrant shape and the maximum diffusion, in which the reentrant shape also displays a critical behavior consistent with the DP universality class (in similarity with the pure model). In order to compare with very recent claims, the results from taking a bimodal distribution and critical behavior in the limit of strong disorder are presented. Also, the results derived from the mean-field theory are performed, presenting partial agreement with numerical results. Lastly, a comparison with the diffusive disordered CP is undertaken.

Modulated systems in external fields: Conditions for the presence of reentrant phase diagrams

We introduce a new coarse grain model capable of describing the phase behavior of two dimensional ferromagnetic systems with competing exchange and dipolar interactions, as well as an external magnetic field. An improved expression for the mean field entropic contribution allows to compute the phase diagram in the whole temperature versus external field plane. We find that the topology of the phase diagram may be qualitatively different depending on the ratio between the strength of the competing interactions. In the regime relevant for ultrathin ferromagnetic films with perpendicular anisotropy we confirm the presence of inverse symmetry breaking from a modulated phase to a homogenous one as the temperature is lowered at constant magnetic field, as reported in experiments. For other values of the competing interactions we show that reentrance may be absent. Comparing thermodynamic quantities in both cases, as well as the evolution of magnetization profiles in the modulated phases, we conclude that the reentrant behavior is a consequence of the suppression of domain wall degrees of freedom at low temperatures at constant fields.

Bridging and depletion mechanisms in colloid-colloid effective interactions: A reentrant phase diagram.

A general class of nonadditive sticky-hard-sphere binary mixtures, where small and large spheres represent the solvent and the solute, respectively, is introduced. The solute-solute and solvent-solvent interactions are of hard-sphere type, while the solute-solvent interactions are of sticky-hard-sphere type with tunable degrees of size nonadditivity and stickiness. Two particular and complementary limits are studied using analytical and semi-analytical tools. The first case is characterized by zero nonadditivity, lending itself to a Percus-Yevick approximate solution from which the impact of stickiness on the spinodal curves and on the effective solute-solute potential is analyzed. In the opposite nonadditive case, the solvent-solvent diameter is zero and the model can then be reckoned as an extension of the well-known Asakura-Oosawa model with additional sticky solute-solvent interaction. This latter model has the property that its exact effective one-component problem involves only solute-solute pair potentials for size ratios such that a solvent particle fits inside the interstitial region of three touching solutes. In particular, we explicitly identify the three competing physical mechanisms (depletion, pulling, and bridging) giving rise to the effective interaction. Some remarks on the phase diagram of these two complementary models are also addressed through the use of the Noro-Frenkel criterion and a first-order perturbation analysis. Our findings suggest reentrance of the fluid-fluid instability as solvent density (in the first model) or adhesion (in the second model) is varied. Some perspectives in terms of the interpretation of recent experimental studies of microgels adsorbed onto large polystyrene particles are discussed.

Re-entrant phase behavior in confined two-patch colloidal particles.

We present a version of density functional approach for the system of patchy colloidal particles confined in slitlike pores with hard walls. Each particle possesses two off-center sites of the types A and B, and in addition to single A-A and B-B bonds, formation of the double A-B-A and B-A-B bonds is allowed. The proposed approach is based on the fundamental measure theory and the second order perturbation theory of Wertheim. For the model in question, a re-entrant phase behavior in a bulk system has been found [Kalyuzhnyi Y. V.; Cummings, P. T., J. Chem. Phys. 2013, 139, 104905] . Our calculations revealed that the re-entrant phase diagrams are also observed in confined systems. The upper critical temperature decreases with the pore width, while the lower critical temperature increases very slightly.

Two-patch colloidal model with re-entrant phase behaviour

We propose a second-order thermodynamic perturbation theory for a hard-sphere patchy colloidal model with two doubly bondable patches of type A and B. AB bonding results in the formation of a three-dimensional network of the particles and AA and BB bonding promotes chain formation. The theory is applied to study the phase behaviour of the model at different values of the potential model parameters. Competition between network and chain formation gives rise to a re-entrant phase behaviour with upper and lower critical points. The model with an additional van der Waals type of interaction may have a re-entrant phase diagram with three critical points and two separate regions of the liquid-gas phase coexistence. We analyze our results in terms of the fractions of the particles in different bonding states and conclude that re-entrant phase coexistence can be seen as a coexistence between a gas phase rich in chain ends and a liquid phase rich in branch points.

Interplay of pH and Binding of Multivalent Metal Ions: Charge Inversion and Reentrant Condensation in Protein Solutions

Tuning of protein surface charge is a fundamental mechanism in biological systems. Protein charge is regulated in a physiological context by pH and interaction with counterions. We report on charge inversion and the related reentrant condensation in solutions of globular proteins with different multivalent metal cations. In particular, we focus on the changes in phase behavior and charge regulation due to pH effects caused by hydrolysis of metal ions. For several proteins and metal salts, charge inversion as measured by electrophoretic light scattering is found to be a universal phenomenon, the extent of which is dependent on the specific protein-salt combination. Reentrant phase diagrams show a much narrower phase-separated regime for acidic salts such as AlCl3 and FeCl3 compared to neutral salts such as YCl3 or LaCl3. The differences between acidic and neutral salts can be explained by the interplay of pH effects and binding of the multivalent counterions. The experimental findings are reproduced with good agreement by an analytical model for protein charging taking into account ion condensation, metal ion hydrolysis, and interaction with charged amino acid side chains on the protein surface. Finally, the relationship of charge inversion and reentrant condensation is discussed, suggesting that pH variation in combination with multivalent cations provides control over both attractive and repulsive interactions between proteins.

Reentrant Wetting of Network Fluids

We use a simple mesoscopic Landau-Safran theory of network fluids to show that a reentrant phase diagram, in the "empty liquid" regime, leads to nonmonotonic surface tension and reentrant wetting, as previously reported for binary mixtures. One of the wetting transitions is of the usual kind, but the low temperature transition may allow the display of the full range of fluctuation regimes predicted by renormalization group theory.

Wave-Packet Dynamics in Chains with Delayed Electronic Nonlinear Response

We study the dynamics of one electron wave packet in a chain with a nonadiabatic electron-phonon interaction. The electron-phonon coupling is taken into account in the time-dependent Schrödinger equation by a delayed cubic nonlinearity. In the limit of an adiabatic coupling, the self-trapping phenomenon occurs when the nonlinearity parameter exceeds a critical value of the order of the bandwidth. We show that a weaker nonlinearity is required to produce self-trapping in the regime of short delay times. However, this trend is reversed for slow nonlinear responses, resulting in a reentrant phase diagram. In slowly responding media, self-trapping only takes place for very strong nonlinearities.

Temperature effects in the mechanical desorption of an infinitely long lattice chain: Re-entrant phase diagrams

We consider the mechanical desorption of an infinitely long lattice polymer chain tethered at one end to an adsorbing surface. The external force is applied to the free end of the chain and is normal to the surface. There is a critical value of the desorption force f(tr) at which the chain desorbs in a first-order phase transition. We present the phase diagram for mechanical desorption with exact analytical solutions for the detachment curve: the dependence of f(tr) on the adsorption energy epsilon (at fixed temperature T) and on T (at fixed epsilon). For most lattice models f(tr)(T) displays a maximum. This implies that at some given force the chain is adsorbed in a certain temperature window and desorbed outside it: the stretched state is re-entered at low temperature. We also discuss the energy and heat capacity as a function of T; these quantities display a jump at the transition(s). We analyze short-range and long-range excluded-volume effects on the detachment curve f(tr)(T). For short-range effects (local stiffness), the maximum value of f(tr) decreases with stiffness, and the force interval where re-entrance occurs become narrower for stiffer chains. For long-range excluded-volume effects we propose a scaling f(tr) approximately T(1-nu)(T(c)-T)(nu/phi) around the critical temperature T(c), where nu=0.588 is the Flory exponent and phi approximately 0.5 the crossover exponent, and we estimated the amplitude. We compare our results for a model where immediate step reversals are forbidden with recent self-avoiding walk simulations. We conclude that re-entrance is the general situation for lattice models. Only for a zigzag lattice model (where both forward and back steps are forbidden) is the coexistence curve f(tr)(T) monotonic, so that there is no re-entrance.

Re-entrant phase diagram and pH effects in cross-linked gelatin gels

Experimental results have shown that the kinetics of bond formation in chemical cross-linking of gelatin solutions are strongly affected not only by gelatin and reactant concentrations but also by the solution pH. We present an extended numerical investigation of the phase diagram and of the kinetics of bond formation as a function of the pH, via Monte Carlo simulations of a lattice model for gelatin chains and reactant agent in solution. We find a re-entrant phase diagram, namely, gelation can be hindered either by loop formation at low reactant concentrations, or by saturation of chain active sites via formation of single bonds with a cross-linker at high reactant concentrations. The ratio of the characteristic times for the formation of the first and the second bond between the cross-linker and an active site of a chain is found to depend on the reactant reactivity, in good agreement with experimental data.

Modelling the adsorption of a polymer subject to an elongational force by directed walk models

We discuss several different directed walk models of a homopolymer adsorbing at a surface when the polymer is subject to an elongational force which hinders the adsorption. These models have the advantage that, within the generating function approach, they can often be solved exactly and that in the stretching regime they give a fair representation of the configurational properties of the polymer. By using combinatorial arguments we analyse how the critical temperature for adsorption depends on the magnitude of the applied force and show that the order of the adsorption transition changes from continuous to first order when a force is applied. We discuss which are the minimal ingredients to add into the model in order to obtain a reentrant phase diagram similar to the one observed in models of DNA mechanical denaturation. Another advantage in using directed walk models is that they can be generalized to study, to some extent, the adsorption transition of random copolymers. Indeed, despite the fact that the quenched model cannot be solved exactly we show that a partial knowledge of the full random problem can be obtained by resorting to an approximation in which the quenched average is approximated by a partial annealing procedure, the so-called Morita approximation.

Orientational Ordering of ortho–para Mixtures of Crystals of Homonuclear Diatomic Molecules: Theoretical Evidence for Reentrance

We have developed a theoretical formalism to calculate the orientational phase diagram of ortho–para (or odd-J/even-J) mixtures of homonuclear diatomic molecules in the low-pressure solid phases. In particular, our formalism allows for the explicit disorder present in such mixtrues. While the formalism is general, here we apply it to the quantum anisotropic planar rotor model, a two-dimensional model of coupled rotors. Our calculated phase diagram, separating phases of disorder and short-range order is reentrant, when an equilibrium mixture of odd-J/even-J species is considered. A reentrant phase diagram separating states of disorder and long-range order is known to exist in all-J species in both two and three dimensions. The phase diagram we find for the thermal mixture of odd-J/even-J species exhibits reentrance over a wider range of coupling constants than the corresponding all-J species. We also investigate systems where the odd-J fraction is fixed as a function of temperature. We find that even 1% odd-J mixture exhibits a phase diagram different from the pure even-J case, indicating that the even-J molecules play important role in orientational ordering.

Theoretical Evidence for a Reentrant Phase Diagram in Ortho-Para Mixtures of SolidH2at High Pressure

We develop a multiorder parameter mean-field formalism for systems of coupled quantum rotors. The scheme is developed to account for systems where ortho-para distinction is valid. We apply our formalism to solid H2 and D2. We find an anomalous reentrant orientational phase transition for both systems at thermal equilibrium. The correlation functions of the order parameter indicate short-range order at low temperatures. As the temperature is increased the correlation increases along the phase boundary. We also find that even extremely small odd-J concentrations (1%) can trigger short-range orientational ordering.

Role of diffusion in branching and annihilation random walk models

Different branching and annihilating random walk models are investigated by the cluster mean-field method and simulations in one and two dimensions. In the case of the A-->2A , 2A--> 0 model the cluster mean-field approximations show diffusion dependence in the phase diagram as was found recently by the nonperturbative renormalization group method [Phys. Rev. Lett. 92, 255703 (2004)]]. The same type of survey for the A-->2A , 4A--> 0 model results in a reentrant phase diagram, similar to that of the 2A-->3A , 4A--> 0 model [Phys. Rev. E 69, 036112 (2004)]]. Simulations of the A-->2A , 4A--> 0 model in one and two dimensions confirm the presence of both the directed percolation transitions at finite branching rates and the mean-field transition at zero branching rate. In two dimensions the directed percolation transition disappears for strong diffusion rates. These results disagree with the predictions of the perturbative renormalization group method.

Critical behavior of the two-dimensional 2A-->3A, 4A--> phi binary system.

The phase transitions of the recently introduced 2A-->3A, 4A--> phi reaction-diffusion model [G. Odor, Phys. Rev. E 69, 036112 (2004)]] are explored in two dimensions. This model exhibits site-occupation restriction and explicit diffusion of isolated particles. A reentrant phase diagram in the diffusion-creation rate space is confirmed, in agreement with cluster mean-field and one-dimensional results. For strong diffusion, a mean-field transition can be observed at zero branching rate characterized by an alpha=1/3 density decay exponent. In contrast, for weak diffusion the effective 2A-->3A-->4A--> phi reaction becomes relevant and the mean-field transition of the 2A-->3A, 2A--> phi model characterized by alpha=1/2 also appears for nonzero branching rates.

Adsorption of a directed polymer subject to an elongational force

We consider several different directed walk models of a homopolymer adsorbing at a surface when the polymer is subject to an elongational force which hinders the adsorption. We use combinatorial methods for analyzing how the critical temperature for adsorption depends on the magnitude of the applied force and show that the crossover exponent changes when a force is applied. We discuss the characteristics of the model needed to obtain a re-entrant phase diagram.