Fluctuation-driven First-order Transition Research Articles

Different critical behaviors in perovskites with a structural phase transition from cubic-to-trigonal and cubic-to-tetragonal symmetry

Perovskites like LaAlO3 (or SrTiO3) undergo displacive structural phase transitions from a cubic crystal to a trigonal (or tetragonal) structure. For many years, the critical exponents in both these types of transitions have been fitted to those of the isotropic three-components Heisenberg model. However, field theoretical calculations showed that the isotropic fixed point of the renormalization group is unstable, and renormalization group iterations flow either to a cubic fixed point or to a fluctuation-driven first-order transition. Here we show that these two scenarios correspond to the cubic to trigonal and to the cubic to tetragonal transitions, respectively. In both cases, the critical behavior is described by slowly varying effective critical exponents, which exhibit universal features. For the trigonal case, we predict a crossover of the effective exponents from their Ising values to their cubic values (which are close to the isotropic ones). For the tetragonal case, the effective exponents can have the isotropic values over a wide temperature range, before exhibiting large changes en route to the first-order transition. New renormalization group calculations near the isotropic fixed point in three dimensions are presented and used to estimate the effective exponents, and dedicated experiments to test these predictions are proposed. Similar predictions apply to cubic magnetic and ferroelectric systems.

Quantum fluctuation-driven first-order phase transitions in optical lattices

We study quantum fluctuation driven first-order phase transitions of a two-species bosonic system in a three-dimensional optical lattice. Using effective potential method we find that the superfluid-Mott insulator phase transition of one type of bosons can be changed from second-order to first-order by the quantum fluctuations of the other type of bosons. The study of the scaling behaviors near the quantum critical point shows that the first-order phase transition has a different universality from the second-order one. We also discuss the observation of this exotic phenomenon in the realistic cold-atom experiments.

Correlation between A-site randomness and magnetic phase transition in half-doped manganite Pr0.5Ba0.5MnO3

The interplay between A-site randomness and magnetic phase transition in half-doped manganite Pr0.5Ba0.5MnO3 (PBMO) was extensively investigated. The H/M versus M2 isotherms show that the A-site ordered PBMO undergoes a second-order magnetic phase transition from paramagnetism to ferromagnetism, whereas the A-site disordered PBMO exhibits a fluctuation-driven first-order transition arising from a competing order phase possibly existing in the paramagnetic state. A step-like transition in magnetization and resistivity with a sharp width of ΔH/H ∼ 10−3 was only observed in the A-site partially ordered PBMO at 2 K, indicating that the metamagnetic transition is associated with a competition between randomly distributed short-range ferromagnetic and antiferromagnetic phases. These findings provide evidence that the A-site randomness not only suppresses A-type antiferromagnetism also moderately weakens long-range ferromagnetism in the A-site ordered PBMO.

Monte Carlo simulations of magnetic ordering in the fcc kagome lattice

Monte Carlo simulation results are reported on magnetic ordering in ABC stacked Kagom\'{e} layers with fcc symmetry for both XY and Heisenberg models which include exchange interactions with the eight near-neighbors. Well known degeneracies of the 2D system persist in the 3D case and analysis of the numerical data provides strong evidence for a fluctuation-driven first-order transition to well-defined long-range order characterized as the layered $q=0$ (120-degree) spin structure. Effects of varying the inter-layer coupling are also examined. The results are relevant to understanding the role of frustration in IrMn$_3$ alloys widely used by the magnetic storage industry as thin-films in the antiferromagnetic pinning layer in GMR and TMR spin valves. Despite the technological importance of this structure, it has not previously been noted that the magnetic Mn-ions of fcc IrMn$_3$ form Kagom\'{e} layers.

Atom-light crystallization of Bose-Einstein condensates in multimode cavities: Nonequilibrium classical and quantum phase transitions, emergent lattices, supersolidity, and frustration

The self-organization of a Bose-Einstein condensate in a transversely pumped optical cavity is a process akin to crystallization: when pumped by a laser of sufficient intensity, the coupled matter and light fields evolve, spontaneously, into a spatially modulated pattern, or crystal, whose lattice structure is dictated by the geometry of the cavity. In cavities having multiple degenerate modes, the quasi-continuum of possible lattice arrangements, and the continuous symmetry breaking associated with the adoption of a particular lattice arrangement, give rise to phenomena such as phonons, defects, and frustration, which have hitherto been unexplored in ultracold atomic settings involving neutral atoms. The present work develops a nonequilibrium field-theoretic approach to explore the self-organization of a BEC in a pumped, lossy optical cavity. We find that the transition is well described, in the regime of primary interest, by an effective equilibrium theory. At nonzero temperatures, the self-organization occurs via a fluctuation-driven first-order phase transition of the Brazovskii class; this transition persists to zero temperature, and crosses over into a quantum phase transition of a new universality class. We make further use of our field-theoretic description to investigate the role of nonequilibrium fluctuations on the self-organization transition, as well as to explore the nucleation of ordered-phase droplets, the nature and energetics of topological defects, supersolidity in the ordered phase, and the possibility of frustration controlled by the cavity geometry. In addition, we discuss the range of experimental parameters for which we expect the phenomena described here to be observable, along with possible schemes for detecting ordering and fluctuations via either atomic correlations or the correlations of the light emitted from the cavity.

Superfluid-insulator transition and fermion pairing in Bose-Fermi mixtures

It is well known that bosons on an optical lattice undergo a second-order superfluid-insulator transition (SIT) when the lattice potential increases. In this paper, we study SIT when fermions coexist with the bosons. We find that the critical properties of particle-hole symmetric SIT with dynamical exponent $z=1$ is modified when fermions are present; it either becomes a fluctuation-driven first-order transition or a different second-order transition. On the other hand, the more generic particle-hole asymmetric (with $z=2$) SIT is stable against coupling with fermions. We also discuss pairing interaction between fermions mediated by quantum critical fluctuations near SIT and show that the fermion pairing and/or superfluid transition temperature peaks near SIT when a single species of fermion is present.

Hexatic-herringbone coupling at the hexatic transition in smectic liquid crystals: 4-epsilon renormalization group calculations revisited.

Simple symmetry considerations would suggest that the transition from the smectic-A phase to the long-range bond-orientationally ordered hexatic smectic-B phase should belong to the XY universality class. However, a number of experimental studies have reported over the past twenty years "novel" critical behavior with non-XY critical exponents for this transition. Bruinsma and Aeppli argued [Phys. Rev. Lett. 48, 1625 (1982)], using a 4-epsilon renormalization-group calculation, that short-range molecular herringbone correlations coupled to the hexatic ordering drive this transition first order via thermal fluctuations, and that the critical behavior observed in real systems is controlled by a "nearby" tricritical point. We have revisited the model of Bruinsma and Aeppli and present here the results of our study. We have found two nontrivial strongly coupled herringbone-hexatic fixed points apparently missed by these authors. Yet, these two nontrivial fixed points are unstable, and we obtain the same final conclusion as the one reached by Bruinsma and Aeppli, namely that of a fluctuation-driven first-order transition. We also discuss the effect of local twofold distortion of the bond order as a possible "extra" order parameter in the Hamiltonian.

Effect of rare locally ordered regions on a disordered itinerant quantum antiferromagnet with cubic anisotropy

We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in the presence of quenched disorder, paying particular attention to the locally ordered spatial regions that form in the Griffiths region. We derive an effective action where these rare regions are described in terms of static annealed disorder. A one loop renormalization group analysis of the effective action shows that for order parameter dimensions $p<4$ the rare regions destroy the conventional critical behavior. For order parameter dimensions $p>4$ the critical behavior is not influenced by the rare regions, it is described by the conventional dirty cubic fixed point. We also discuss the influence of the rare regions on the fluctuation-driven first-order transition in this system.

Kinetics of ordering in fluctuation-driven first-order transitions: simulation and theory

Many systems involving competing interactions or interactions that compete with constraints are well described by a model first introduced by Brazovskii [Zh. Eksp. Teor. Fiz. 68, 175 (1975) [Sov. Phys. JETP 41, 85 (1975)]]. The hallmark of this model is that the fluctuation spectrum is isotropic and has a maximum at a nonzero wave vector represented by the surface of a d-dimensional hypersphere. It was shown by Brazovskii that the fluctuations change the free energy structure from a straight phi(4) to a straight phi(6) form with the disordered state metastable for all quench depths. The transition from the disordered phase to the periodic lamellar structure changes from second order to first order and suggests that the dynamics is governed by nucleation. Using numerical simulations we have confirmed that the equilibrium free energy function is indeed of a straight phi(6) form. A study of the dynamics, however, shows that, following a deep quench, the dynamics is described by unstable growth rather than nucleation. A dynamical calculation, based on a generalization of the Brazovskii calculations, shows that the disordered state can remain unstable for a long time following the quench.

External-Field-Induced Tricritical Point in a Fluctuation-Driven Nematic–Smectic-ATransition

We study theoretically the effect of an external field on the nematic-smectic-A (NA) transition close to the tricritical point, where fluctuation effects govern the qualitative behavior of the transition. An external field suppresses nematic director fluctuations, by making them massive. For a fluctuation-driven first-order transition, we show that an external field can drive the transition second-order. In an appropriate liquid crystal system, we predict the required magnetic field to be of order 10 T. The equivalent electric field is of order $1 V/\mu m$.

Quenched randomness at first-order transitions

A rigorous theorem due to Aizenman and Wehr asserts that there can be no latent heat in a two-dimensional system with quenched random impurities. We examine this result, and its possible extensions to higher dimensions, in the context of several models. For systems whose pure versions undergo a strong first-order transition, we show that there is an asymptotically exact mapping to the random field Ising model, at the level of the interface between the ordered and disordered phases. This provides a physical explanation for the above result and also implies a correspondence between the problems in higher dimensions, including scaling relations between their exponents. The particular example of the q-state Potts model in two dimensions has been considered in detail by various authors and we review the numerical results obtained for this case. Turning to weak, fluctuation-driven first-order transitions, we describe analytic renormalization group calculations which show how the continuous nature of the transition is restored by randomness in two dimensions.

Effect of random impurities on fluctuation-driven first-order transitions

We analyse the effect of quenched uncorrelated randomness coupling to the local energy density of a model consisting of N coupled two-dimensional Ising models. For N>2 the pure model exhibits a fluctuation-driven first order transition, characterised by runaway renormalisation group behaviour. We show that the addition of weak randomness acts to stabilise these flows, in such a way that the trajectories ultimately flow back towards the pure decoupled Ising fixed point, with the usual critical exponents alpha=0, nu=1, apart from logarithmic corrections. We also show by examples that, in higher dimensions, such transitions may either become continuous or remain first order in the presence of randomness.

Metastability in fluctuation-driven first-order transitions: Nucleation of lamellar phases.

The nucleation of a lamellar phase from a supercooled homogeneous phase in a fluctuation driven first-order transition is studied, based on a phenomenological free energy due to Brazovskii. The absence of phase coexistence in the corresponding mean-field approximation makes application of the standard droplet theory of homogeneous nucleation problematic. A self-consistent coarse-graining procedure is introduced to overcome this difficulty, and the barrier height for nucleation of a critical droplet is estimated in the weak-coupling limit. Contrary to earlier estimates the critical droplet shape is shown to be anisotropic in general. Some effects of distortions and defects in the lamellar structure are considered and are shown to affect the critical droplet only very near coexistence where the probability of nucleation vanishes. The coarse-graining procedure introduced here follows from a novel application of the momentum-shell renormalization group method to systems in the Brazovskii class. Possible applications of the theory to the microphase separation transition in diblock copolymers and to Rayleigh-B\'{e}nard convection are briefly discussed.

Phase transitions in anisotropic superconducting and magnetic systems with vector order parameters: Three-loop renormalization-group analysis.

The critical behavior of a model with N-vector complex order parameter and three quartic coupling constants that describes phase transitions in unconventional superconductors, helical magnets, stacked triangular antiferromagnets, superfluid helium-3, and zero-temperature transitions in fully frustrated Josephson-junction arrays is studied within the field- theoretical renormalization-group approach in three dimensions. To obtain qualitatively and quantitatively correct results perturbative expansions for \beta-functions and critical exponents are calculated up to three-loop order and resummed by means of the generalized Pade-Borel procedure. Fixed-point coordinates, critical exponent values, RG flows, etc. are found for the physically interesting cases N = 2 and N = 3. Marginal values of N at which the topology of the flow diagram changes are determined as well. In most cases the systems mentioned are shown to undergo fluctuation-driven first-order phase transitions. Continuous transitions are allowed in hexagonal d-wave superconductors, in planar helical magnets (into sinusoidal linearly-polarized phase), and in triangular antiferromagnets (into simple unfrustrated ordered states) with critical exponents \gamma = 1.336, \nu = 0.677, \alpha = -0.030, \beta = 0.347, \eta = 0.026, which are hardly believed to be experimentally distinguishable from those of the 3D XY model. The chiral fixed point of RG equations is found to exist and possess some domain of attraction provided N > 3. Thus, magnets with Heisenberg (N = 3) and XY-like (N = 2) spins should not demonstrate chiral critical behavior with unusual critical exponents; they can approach the chiral state only via first-order phase transitions.

Fluctuation-induced first-order transitions in unconventional superconductors.

Generalized Ginzburg-Landau models of complex-vector order parameters are investigated by the mean-field approximation and the renormalization-group theory. Mean-field results for the possible ordered phases and their domains of stability are presented. The availability of large regions on the phase diagram in which the phase transitions are of first order is established. The fixed points of the renormalization-group equations and their stability properties are investigated up to second order in \ensuremath{\epsilon}=4-d. Except for systems with cubic anisotropy, the renormalization-group equations do not have stable fixed points, and this indicates the presence of fluctuation-driven first-order transitions. For cubic symmetries a new critical behavior is reported. The results are related to superconductivity in high-${\mathit{T}}_{\mathit{c}}$ oxides and heavy-fermion systems.

Self-avoiding walks and manifolds in random environments.

Self-avoiding walks (SAW's) and manifolds (SAM's) in random environments are studied using a combination of Lifshitz arguments and field-theoretic methods. The number of N-step SAW's starting at the origin, Z, is shown to be a broadly distributed quantity whose typical value, ${\mathit{Z}}_{\mathrm{typ}}$, behaves as ${\mathit{Z}}_{\mathrm{typ}}$\ensuremath{\sim}〈Z〉exp(-${\mathit{cN}}^{\mathrm{\ensuremath{\alpha}}}$) below four dimensions. Here \ensuremath{\alpha}=2-d\ensuremath{\nu} and 〈Z〉 is the average number of SAW's at the origin. On the other hand, the integer moments of Z are exponentially larger than the average, i.e., 〈${\mathit{Z}}^{\mathit{k}}$〉\ensuremath{\sim}〈Z${\mathrm{〉}}^{\mathit{k}}$exp[${\mathit{ck}}^{1/\mathrm{\ensuremath{\alpha}}}$(k-1)N] for the range 1k${\mathit{k}}_{\mathit{c}}$. Similar results hold for SAM's. Within the field theory for SAW's the results for 1k${\mathit{k}}_{\mathit{c}}$ arise from a fluctuation-driven first-order phase transition in the k-replicated theory. Above ${\mathit{k}}_{\mathit{c}}$, Griffiths singularities control the moments of Z.

The effect of impurities on the R-point instability in KMnF3. I. An X-ray scattering study

The wavevector dependence of the critical fluctuations at the cubic-to-tetragonal structural phase transition in KMnF3 doped with 1% and 10% of KMgF3 has been studied using X-ray scattering techniques. It is found that the introduction of impurities lowers Tc and that the fluctuation-driven first-order transition becomes continuous when the impurity concentration exceeds a certain threshold. At temperatures far above Tc, the temperature dependence of the X-ray critical scattering cross section measured in the samples KMnF3, KMn0.99Mg0.01F3 and KMn0.9Mg0.1F3 is described by the same critical exponents nu and gamma . Contrary to expectation, the magnitude of the anomalous narrow component observed in the critical scattering in pure KMnF3 close to Tc is significantly reduced by the introduction of the impurities.

Effect of impurities on the first-order phase transition of KMnF3.

The phase transitions at the $R$ point in KMn${\mathrm{F}}_{3}$ doped with 1% and 10% of KMg${\mathrm{F}}_{3}$, with 1% of NaMn${\mathrm{F}}_{3}$, and with 1% of KCa${\mathrm{F}}_{3}$, have been studied with x-ray scattering techniques. The Mg impurities lower ${T}_{c}$ while the others raise ${T}_{c}$, by amounts which are roughly consistent with the differences in the atomic radii. In both cases it is found that the fluctuation-driven first-order transition becomes continuous when the concentration of impurity exceeds a critical amount.

Ab initio determination of a structural phase transition temperature.

The temperature of the structural phase transition in GeTe is calculated complete ab initio from a model lattice-dynamical Hamiltonian that is constructed from microscopic quantum-mechanical total-energy calculations. The phase transition in the model system is studied through a renormalization-group-theory approach, leading to the prediction of a fluctuation-driven first-order transition at 657\ifmmode\pm\else\textpm\fi{}100 K.

Fluctuation driven first-order phase transition, below four dimensions, in the random-field Ising model with a Gaussian random-field distribution.

Analysis of the high-temperature susceptibility series for the random-field Ising model with a Gaussian distribution of random fields demonstrates the existence of a fluctuation-driven first-order transition below four dimensions, $d&lt;4$. This, and the behavior of the susceptibility exponent in three dimensions, suggest that $d=4$ is a "critical" dimension for the model.