Continuous Melting Transition Research Articles

First-order and continuous melting transitions in two-dimensional Lennard-Jones systems and repulsive disks.

In two-dimensional Lennard-Jones (LJ) systems, a small interval of melting-mode switching occurs below which the melting occurs by first-order phase transitions in lieu of the melting scenario proposed by Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY). The extrapolated upper bound for phase coexistence is at density ρ∼0.893 and temperature T∼1.1, both in reduced LJ units. The two-stage KTHNY scenario is restored at higher temperatures, and the isothermal melting scenario is universal. The solid-hexatic and hexatic-liquid transitions in KTHNY theory, even so continuous, are distinct from typical continuous phase transitions in that instead of scale-free fluctuations, they are characterized by unbinding of topological defects, resulting in a special form of divergence of the correlation length: ξ≈exp(b|T-T_{c}|^{-ν}). Here such a divergence is firmly established for a two-dimensional melting phenomenon, providing a conclusive proof of the KTHNY melting. We explicitly confirm that this high-temperature melting behavior of the LJ system is consistent with the melting behavior of the r^{-12} potential and that melting of the r^{-n} potential is KTHNY-like for n≤12 but melting of the r^{-64} potential is first order; similar to hard disks. Therefore we suggest that the melting scenario of these repulsive potentials becomes hard-disk-like for an exponent in the range 12<n<64.

Nature of two-dimensional melting in simple atomic systems

We investigate the characteristics of two-dimensional melting in simple atomic systems via isobaric-isothermal (NPT) and isochoric-isothermal (NV T) molecular dynamics simulations with a special focus on the effect of the range of the potential on the melting. We find that the system with an interatomic potential of longer range clearly exhibits a region (in the PT plane) with a (thermodynamically) stable hexatic phase. On the other hand, the system with a shorter-range potential exhibits a first-order melting transition both in the NPT and the NV T ensembles. Melting of the system with an intermediate range potential shows a hexatic-like feature near the melting transition in the NV T ensemble, but it undergoes an unstable hexatic-like phase during melting process in the NPT ensemble, which implies the existence of a weakly first-order transition. The overall features represent a crossover from a continuous melting transition in the cases of longer-ranged potentials to a discontinuous (first-order) one in the systems with shorter and intermediate ranged potentials. We also calculate the Binder cumulants, as well as the susceptibility, of the bond-orientational order parameter.

On the metastability of the hexatic phase during the melting of two-dimensional charged particle solids

For two-dimensional many-particle systems first-order, second-order, single step continuous, as well as two-step continuous (KTHNY-like) melting transitions have been found in previous studies. Recent computer simulations, using particle numbers in the $\geq 10^5$ range, as well as a few experimental studies, tend to support the two-step scenario, where the solid and liquid phases are separated by a third, so called hexatic phase. We have performed molecular dynamics simulations on Yukawa (Debye-H\"uckel) systems at conditions earlier predicted to belong to the hexatic phase. Our simulation studies on the time needed for the equilibration of the systems conclude that the hexatic phase is metastable and disappears in the limit of long times. We also show that simply increasing the particle number in particle simulations does not necessarily result in more accurate conclusions regarding the existence of the hexatic phase. The increase of the system size has to be accompanied with the increase of the simulation time to ensure properly thermalized conditions.

Stripe melting and quantum criticality in correlated metals

We study theoretically quantum melting transitions of stripe order in a metallic environment, and the associated reconstruction of the electronic Fermi surface. We show that such quantum phase transitions can be continuous in situations where the stripe melting occurs by proliferating pairs of dislocations in the stripe order parameter without proliferating single dislocations. We develop an intuitive picture of such phases as "Stripe Loop Metals" where the fluctuating stripes form closed loops of arbitrary size at long distances. We obtain a controlled critical theory of a few different continuous quantum melting transitions of stripes in metals . At such a (deconfined) critical point the fluctuations of the stripe order parameter are strongly coupled, yet tractable. They also decouple dynamically from the Fermi-surface. We calculate many universal properties of these quantum critical points. In particular we find that the full Fermi-surface and the associated Landau quasiparticles remain sharply defined at the critical point. We discuss the phenomenon of Fermi surface reconstruction across this transition and the effect of quantum critical stripe fluctuations on the superconducting instability. We study possible relevance of our results to several phenomena in the cuprates.

Continuous thermal melting of a two-dimensional Abrikosov vortex solid

We examine the question of thermal melting of the triangular Abrikosov vortex solid in two-dimensional superconductors or neutral superfluids. We introduce a model, which combines lowest Landau level (LLL) projection with the magnetic Wannier basis to represent degenerate eigenstates in the LLL. Solving the model numerically via large-scale Monte Carlo simulations, we find clear evidence for a continuous melting transition, in perfect agreement with the Kosterlitz-Thouless-Halperin-Nelson-Young theory and with recent experiments.

Electromagnetic Coulomb gas with vector charges and “elastic” potentials: Renormalization group equations

We present a detailed derivation of the renormalization group equations for two-dimensional electromagnetic Coulomb gases whose charges lie on a triangular lattice (magnetic charges) and its dual (electric charges). The interactions between the charges involve both angular couplings and a new electromagnetic potential. This motivates the denomination of “elastic” Coulomb gas. Such elastic Coulomb gases arise naturally in the study of the continuous melting transition of two-dimensional solids coupled to a substrate, either commensurate or with quenched disorder.

Ab Initio Molecular Dynamical Investigation of the Finite Temperature Behavior of the Tetrahedral Au19 and Au20 Clusters

Density functional molecular dynamics simulations have been carried out to understand the finite temperature behavior of Au19 and Au20 clusters. Au20 has been reported to be a unique molecule having tetrahedral geometry, a large HOMO-LUMO energy gap, and an atomic packing similar to that of the bulk gold (Li, J.; et al. Science 2003, 299, 864). Our results show that the geometry of Au19 is exactly identical with that of Au20 with one missing corner atom (called a vacancy). Surprisingly, our calculated heat capacities for this nearly identical pair of gold clusters exhibit dramatic differences. Au20 undergoes a clear and distinct solid-like to liquid-like transition with a sharp peak in the heat capacity curve around 770 K. On the other hand, Au19 has a broad and flat heat capacity curve with continuous melting transition. This continuous melting transition turns out to be a consequence of a process involving a series of atomic rearrangements along the surface to fill in the missing corner atom. This results in a restricted diffusive motion of atoms along the surface of Au19 between 650 to 900 K during which the shape of the ground state geometry is retained. In contrast, the tetrahedral structure of Au20 is destroyed around 800 K, and the cluster is clearly in a liquid-like state above 1000 K. Thus, this work clearly demonstrates that (i) the gold clusters exhibit size sensitive variations in the heat capacity curves and (ii) the broad and continuous melting transition in a cluster, a feature that has so far been attributed to the disorder or absence of symmetry in the system, can also be a consequence of a defect (absence of a cap atom) in the structure.

Decoupled two-dimensional superconductivity and continuous melting transitions in layered superconductors immersed in a parallel magnetic field

Possible phases and the B-T phase diagram of interlayer Josephson vortices induced by a magnetic field parallel to the superconducting layers are investigated by Monte Carlo simulations based on the anisotropic, frustrated XY model. While for low magnetic fields and small anisotropy parameters a single first-order transition is observed similarly to the melting of Abrikosov (or pancake) vortex lattice, an intermediate phase, characterized by decoupled, two-dimensional (2D) quasi long-range crystalline order (QLRCO) and superconductivity, is found at high magnetic fields and large anisotropy parameters. Combining the simulation results with a symmetry argument, it is revealed that this intermediate phase is of Kosterlitz-Thouless (KT) type, and the melting of 2D quasi Josephson vortex lattices and suppression of superconductivity is a KT transition. Evolution of the intermediate phase to the low-temperature phase of 3D LRCO is second order and belongs to the 3D XY universality class. The three phase boundaries merge at a multicritical point. It is revealed that decoupling of the 3D Josephson vortex lattice into the 2D phase is triggered by hops of Josephson flux lines across superconducting layers activated by thermal fluctuations. The equilibrium phase diagram with the KT phase at high magnetic fields and large anisotropy parameters is consistent with the peculiar Lorentz-force-independent dissipation observed in highly anisotropic high-Tc superconductor Bi2Sr2CaCu2O(8+y) by Iye et al. (Physica 159C, 433 (1989)).

Continuous melting of compact polymers.

The competition between chain entropy and bending rigidity in compact polymers can be addressed within a lattice model introduced by Flory in 1956 [Proc. R. Soc. London A 234, 60 (1956)]]. It exhibits a transition between an entropy dominated disordered phase and an energetically favored crystalline phase. The nature of this order-disorder transition has been debated ever since the introduction of the model. Here we present exact results for the Flory model in two dimensions relevant for polymers on surfaces, such as DNA adsorbed on a lipid bilayer. We predict a continuous melting transition and compute exact values of critical exponents at the transition point.

Vortex-melting and vortex-glass transitions in a high purity twinnedYBa2Cu3O7−δsingle crystal

We present experimental evidence for the coexistence of a first-order vortex-lattice melting transition and a continuous vortex-glass melting transition at a lower temperature in high purity twinned ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ single crystal samples grown in ${\mathrm{BaZrO}}_{3}$ crucibles. The correlation of temperature T and magnetic field H dependence of the electrical resistivity $\ensuremath{\rho}$ and electric field vs current density E vs J isotherms is consistent with a two-step phase transition from the normal to the superconducting state. Analysis of the data strongly indicates that the vortex matter in the single crystal is inhomogeneous. This scenario is supported by the observation of a vortex-lattice melting at a temperature separating two vortex-glass states with different critical exponents $\ensuremath{\nu}(z\ensuremath{-}1).$ In light of independently performed numerical simulations [Crabtree et al., Phys. Rev. B 61, 1446 (2000)], the data support a scenario where the intermediate phase crosses over from a state where vortex lines in the twin boundaries are pinned and those within the bulk undergo driven plastic vortex flow, to a state where the vortex lines in and near the twin boundaries undergo driven disordered motion and those within the bulk move as an ordered lattice.

A KT Phase of Interlayer Josephson Vortex Systems in High-Tc Superconductors

A novel Kosterlitz–Thouless phase and continuous melting transitions are proposed for Josephson vortex systems induced in layered superconductors by strong parallel magnetic fields. The mechanism of the phenomenon is revealed and the phase diagram with a multicritical point is presented.

Continuous melting of a partially pinned two-dimensional vortex lattice in a square array of pinning centers

The structure and equilibrium properties of a two-dimensional system of superconducting vortices in a periodic pinning potential with square symmetry are studied numerically. For a range of the strength of the pinning potential, the low-temperature crystalline state exhibits only one of the two basic periodicities (in the $x$- and $y$-directions) of the pinning potential. This ``partially pinned'' solid undergoes a continuous melting transition to a weakly modulated liquid as the temperature is increased. A spin model, constructed using symmetry arguments, is shown to reproduce the critical behavior at this transition.

Melting Dynamics in Thermal and Stress Driven Coulomb Clusters

The microscopic dynamical responses of a two dimensional circular Coulomb cluster to thermal excitations and to the external force along a narrow band through its center are studied. The strong competition between the cirular boundary and the inner domain with triagular lattice leads to the nonuniform melting of the cluster. With the increasing temperature, the surface particles exhibit anisotropic motions along the circular shells. No abrupt melting transition is observed for the outer region. The intrinsic defects around the domain boundary initiate the continuous core melting transition and also the fluidization under the external stress. The fluidization shows a non equilibrium second order transition with stick-slip type motion at the transition point.

Degradation of phase coherence by defects in a two-dimensional vortex lattice.

The thermodynamic nature of two-dimensional vortex matter is studied through a duality analysis of the XY model over the square lattice with low uniform frustration. A phase-coherent vortex lattice state is found at low temperature if rigid translations are prohibited. It shows a nonzero phase rigidity that is degraded exclusively by the creation of dislocation pairs. The unbinding of such pairs causes the vortex lattice to simultaneously lose phase coherence and to melt at a continuous (Kosterlitz-Thouless) phase transition. General phase autocorrelation functions are also computed, and these results are used to argue for the existence of a continuous melting transition of vortex matter in layered superconductors.

Comment on “One-Stage Continuous Melting Transition in Two Dimensions”

A Comment on the Letter by Julio F. Fern\'andez, Juan J. Alonso, and Jolanta Stankiewicz, Phys. Rev. Lett. 75, 3477 (1995). The authors of the Letter offer a Reply.

One-stage continuous melting transition in two dimensions.

Monte Carlo results are reported for melting of two-dimensional systems of $N$ hard disks for various values of $N$. Runs of up to 1${0}^{8}$ Monte Carlo sweeps give the following equilibrium results: (1) there is a single second-order transition at volume ${\ensuremath{\upsilon}}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.260\ifmmode\pm\else\textpm\fi{}0.005$; (2) the orientational order parameter drops discontinuously to zero at $\ensuremath{\upsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\upsilon}}_{c}$; (3) ${\ensuremath{\eta}}_{6}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.30\ifmmode\pm\else\textpm\fi{}0.05$ at $\ensuremath{\upsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\upsilon}}_{c}$; (4) there is consistency with $\ensuremath{\xi}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{exp}({b/u}^{1/2})$ in the isotropic phase, where $u\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\upsilon}\ensuremath{-}{\ensuremath{\upsilon}}_{c}$ and $b\ensuremath{\simeq}0.8$. An intermediate phase in which the volume can vary by more than about 1% is ruled out.

Structure and phase diagram of tetramethylgermanium adsorbed on graphite (0001) planes

X-ray scattering experiments have been performed on tetramethylgermanium (TMG) physisorbed on (0001) planes of exfoliated graphite (papyex). At coverages below 0.9 monolayers (ML) and temperatures below T = 130 K, TMG adsorbs in a commensurate √7 × √7 structure. A first-order phase transition near T = 110 K leads to a uniaxially compressed phase of the adsorbate with a dipod down structure. In the region of 1 ML and below T = 150 K, TMG forms an incommensurate hexagonal structure and undergoes a transition to the incommensurate dipod down structure at T = 130 K. A continuous melting transition of the two-dimensional structure has been observed for all investigated coverages.

Freezing and melting water in lamellar structures

The manner in which ice forms in lamellar suspensions of dielaidoylphosphatidylethanolamine, dielaidoylphosphatidylcholine, and dioleoylphosphatidylcholine in water depends strongly on the water fraction. For weight fractions between 15 and 9%, the freezing and melting temperatures are significantly depressed below 0 degree C. The ice exhibits a continuous melting transition spanning as much as 20 degrees C. When the water weight fraction is below 9%, ice never forms at temperatures as low as -40 degrees C. We show that when water contained in a lamellar lipid suspension freezes, the ice is not found between the bilayers; it exists as pools of crystalline ice in equilibrium with the bound water associated with the polar lipid headgroups. We have used this effect, together with the known chemical potential of ice, to measure hydration forces between lipid bilayers. We find exponentially decaying hydration repulsion when the bilayers are less than about 7 A apart. For larger separations, we find significant deviations from single exponential decay.

Phase transitions of ethylene monolayers on graphite

Low-energy electron diffraction (LEED) measurements have detected seven solid phases for monolayer ethylene on graphite. Electron-beam induced effects (which presumably include decomposition and/or polymerization of the adsorbed ethylene) were minimized by exposing the adsorbed layer to the nanoamp beam for &amp;lt;100 s per crystal; data were obtained from four different crystals. We concentrate here on the phase transitions from the molecular-axisorientationally disordered low density (DLD) phase to the newly discovered commensurate molecular-axis-disordered low density (CDLD) phase and on the melting of the CDLD phase. The change in the principle q vector in the DLD-CDLD phase transition is presented for several different coverages. These data indicate an interesting incommensurate–commensurate (IC–C) transition which has not been suspected from previous studies. This transition preempts the melting transition: as a consequence we can rule out the possibility of a continuous melting transition as suggested by earlier heat capacity and neutron scattering experiments. In addition, LEED images of the fluid phase produced by melting of the CDLD phase are presented which show a modulated-ring-type structure.

Ethylene on graphite: A low-energy electron-diffraction study.

Several phases of monolayer ethylene on single-crystal graphite have been studied using low-energy electron diffraction. We have determined the unit cell and orientation with respect to the graphite substrate of the orientationally ordered and disordered low-density phases (OLD and DLD), in which molecules are believed to lie with the C?C bond parallel to the surface. Based on published neutron-scattering results, we propose a basis for the OLD phase. The low-coverage DLD phase, believed to undergo a continuous melting transition at 70 K, appears to be a higher-order commensurate structure at this transition. We also report observations of ordered and disordered high-density phases in which molecules stand on end, in both commensurate and incommensurate epitaxies.