Spin-glass energy landscape

We consider a nearest-neighbor-interaction ±J Ising spin glass in a square lattice. Inspired by natural evolution, we design a dynamic rule that includesselection, randomness, andmultibranch exploration. Following this rule, we succeed in walking along the space of states between local energy maxima and minima alternately. During the walk, we store various information about the spin states corresponding to these minima and maxima for later statistical analysis. In particular, we plot a histogram displaying how many times each minimum (or maximum) energy is visited as a function of the corresponding density value. Through finite-size scaling analysis, we conclude that a nonvanishing fraction of bonds remains unsatisfied (satisfied) at these energy minimum (maximum) states in the thermodynamic limit. This fraction measures the degree of unavoidable frustration of the system. Also in this limit, the width of these histograms vanishes, meaning that almost all metastable states occur at the same energy density value, with no dispersion.     

Metastability of Ising spin chains with nearest—neighbour and next—nearest—neighbour interactions in random fields

One-dimensional Ising systems in random fields (RFs) are studied taking into account the nearest-neighbour and next-nearest-neighbour interactions. We investigate two distributions of RFs: binary and Gaussian distributions. We consider four cases of the exchange couplings: ferro－ferromagnetic (F－F), ferro－antiferromagnetic (F－AF), antiferro－ferromagnetic (AF－F) and antiferro－antiferromagnetic (AF－AF). The energy minima of chains of no more than 30 spins with periodic boundary conditions are analysed exactly. We found that the average number of energy minima grows exponentially with the number of spins in both cases of RFs. The energy distributions across the corresponding energy minima are shown. The effects of RFs on both the average and density of metastable states are explained. For a weak RF, the energy distributions display a multipartitioned structure. We also discuss the frustration effect due to RFs and exchange fields. Finally, the distributions of magnetization are calculated. The absolute value of magnetization averaged over all metastable states decreases logarithmically with the number of spins.     

On the theory of superfluidity

We investigate the properties of dispersion spectra of one-dimensional periodic Bose systems with repulsive interparticle interactions. These systems with sufficient large interactions can support metastable supercurrent states, which correspond to the local minima of the dispersion spectra at non-zero momenta. The existence of local minima in the spectra and the energy barriers, which separate the minima, can be explained in terms of Bose exchange symmetry. We extend our study to the case of higher dimensional Bose systems. We suggest that superfluidity could be understood as a Bose exchange effect.     

Static Properties of Potts Spin Chains

One-dimensional 2-state Potts spin glasses (SG) disordered ferromagnets (DFM) and ±J systems are studied. The energy minima (EM) and magnetization with their distributions are exactly calculated. The stable local EM of no more than 27-spin chains with periodic boundary conditions are analyzed. All these systems have an exponentially growing numbers of average energy minima versus number of spins. The frustration effect is also discussed for some particular samples. The investigation of metastable states shows that the energy minima distributions for all our systems approach the normal distribution. The SG and DFM have identical distributions of energy minima. The systems studied here differ merely by the properties of the magnetization. The absolute value of magnetization averaged over all the EM decreases logarithmically with the number of spins for the three systems.     

Computer search for defects in a D = 3 Heisenberg spin glass

A computer study of T = 0 metastable states (local minima) of a Heisenberg spin glass (1728 fixed-length spins on a simple cubic latice with random nearest-neighbor bonds) is reported, in which an attempt is made to describe the relation of nearby minima in terms of defects and to characterize those defects. The local rotation matrix relating one equilibrium configuration to another is well defined, and has a (relatively long) correlation length of 3–4 lattice units. The size of the clusters of spins which tend to be locked together in rigid rotations is 100–200 spins by several criteria. It is found that disclination lines and continuous twists of 360° across the sample exist as stable minima of the energy. However, the domain walls, across which the rotation matrix undergoes a reflection, appear to be more “fundamental” defects. The excitation energy of a defect is of the order of one exchange coupling or less. It does not seem possible to resolve the differences between two metastable states as a simple combination of spatially isolated defects.     

Barriers in the p-spin interacting spin-glass model: the dynamical approach

We investigate the barriers separating metastable states in the spherical p-spin glass model using the instanton method. We show that the problem of finding the barrier heights can be reduced to the causal two-real-replica dynamics. We find the probability for the system to escape one of the highest energy metastable states and the energy barrier corresponding to this process.     

Metastable states of molecules

We define metastable states to be density matrices which are at local minima of a certain non-linear functional, and investigate their general properties, proving in particular that the metastable states are not necessarily unique but are modified Gibbs states. The case of an atom in an external electric field is investigated in some detail.     

Metastable states of spin glasses on random thin graphs

In this paper we calculate the mean number of metastable states for spin glasses on so called random thin graphs with couplings taken from a symmetric binary distribution . Thin graphs are graphs where the local connectivity of each site is fixed to some value c. As in totally connected mean field models we find that the number of metastable states increases exponentially with the system size. Furthermore we find that the average number of metastable states decreases as c in agreement with previous studies showing that finite connectivity corrections of order 1/c increase the number of metastable states with respect to the totally connected mean field limit. We also prove that the average number of metastable states in the limit is finite and converges to the average number of metastable states in the Sherrington-Kirkpatrick model. An annealed calculation for the number of metastable states of energy E is also carried out giving a lower bound on the ground state energy of these spin glasses. For small c one may obtain analytic expressions for . Received 14 October 1999 and Received in final form 14 December 1999     

Thermodynamic Properties of Inhomogeneous Structures in Supercooled Liquids

The weighted density-functional theory is applied to investigate the free-energy landscape of dense supercooled liquids. Metastable states intermediate to the liquid and crystal phases are found, which can be identified with the supercooled states seen in computer simulations. These states are marked by a lower degree of mass localization as compared to the highly localized state termed as "hard-sphere glass" found in earlier studies. We evaluate the free energy using the modified weighted density approximation (MWDA), as formulated by Denton and Ashcroft (1989) Phys. Rev. A , 39 , 4701. The inhomogeneous density is parametrized in terms of Gaussian profiles centered around random lattice sites. The effects of heterogeneity coming from a fluctuation of the width of these Gaussian profiles show that the free energy of the system increases with increase in the fluctuations and, finally, the metastable minima disappear with growing fluctuations.     

Spin-dependent resistivity at transitions between integer quantum hall states

The longitudinal resistivity at transitions between integer quantum Hall states in two-dimensional electrons confined to AlAs quantum wells is found to depend on the spin orientation of the partially filled Landau level in which the Fermi energy resides. The resistivity can be enhanced by an order of magnitude as the spin orientation of this energy level is aligned with the majority spin. We discuss possible causes and suggest a new explanation for the spikelike features observed at the edges of quantum Hall minima near Landau level crossings.     

Importance of metastable states in the free energy landscapes of polypeptide chains

We show that the interplay between excluded volume effects, hydrophobicity, and hydrogen bonding in a tubelike representation of a polypeptide chain gives rise to free energy landscapes that, in addition to a clear global minimum, are characterized by the general presence of a small number of metastable minima, which correspond to common structural motifs observed in proteins. The complexity of the landscape increases only moderately with the length of the chain. Analysis of the temperature dependence of these landscapes reveals that the stability of specific metastable states is maximal at a temperature close to the midpoint of folding. These mestastable states are therefore likely to be of particular significance in determining the generic tendency of proteins to aggregate into potentially pathogenic agents.     

Influence of spin–orbit interactions on the polaron properties in wurtzite semiconductor quantum well

We have study the simultaneous effect of Rashba and Dresselhaus spin–orbit interactions on the polaron properties in wurtzite semiconductor quantum wells. The linear and cubic contributions of the bulk Dresselhaus spin–orbit coupling and the effects of phonon confinement on electron–optical-phonon interaction Hamiltonians are taken into account. We have found analytical solutions for the polaron energies as well as polaron effective mass within the range of validity of perturbation theory. It is shown that the polaron energy and effective mass correction are both significantly enhanced by the spin–orbit coupling. Wave number dependent phonon contribution on the electron energy has minima and varies differently of the spin-up and spin-down states. Polaron self-energy due to interface optical phonon modes has larger values than of the confined optical phonon modes ones. The polaron effective mass exhibits anisotropy and the contribution of the Dresselhaus spin–orbit coupling term on the polaron effective mass is dominated by Rashba one.     

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998     

Excitonic effects in core-excitation spectra of semiconductors

Computer simulations of a model glass-forming system are presented, which study the correlation between the dynamics in real space and the topography of the potential energy landscape. This analysis clearly reveals that in the supercooled regime the dynamics is strongly influenced by the presence of deep valleys in the energy landscape, corresponding to long-lived metastable amorphous states. We explicitly relate nonexponential relaxation effects and dynamic heterogeneities to these metastable states and thus to the specific topography of the energy landscape.     

Analytical potentials for triatomic molecules from spectroscopic data

A general procedure has been developed for constructing analytical potential functions for triatomic molecules which have more than one minimum, these minima not necessarily being related by symmetry. Explicit potentials have been derived for the ground states of HO₂, SO₂ and ClO₂. For HO₂ a linear hydrogen bonded structure O-H----O is predicted as a metastable species. In the case of SO₂ a second minimum corresponding to the species SOO is predicted and ab initio calculations at the SCF MO double-zeta level have been made to establish the geometry and energy of this. For ClO₂ it has been assumed that the spectroscopically observed states of OClO and ClOO are separate minima on the same surface.     

Metastable domain wall dynamics in magnetic nanowires

We study the formation and control of metastable states of pairs of domain walls in cylindrical nanowires of small diameter where the transverse walls are the lower energy state. We show that these pairs form bound states under certain conditions, with a lifetime as long as 200 ns, and are stabilized by the influence of a spin polarized current. Their stability is analyzed with a model based on the magnetostatic interaction and by 3D micromagnetic simulations. The apparition of bound states could hinder the operation of devices.     

Random walk over basins of attraction to construct ising energy landscapes

An efficient algorithm is developed to construct disconnectivity graphs by a random walk over basins of attraction. This algorithm can detect a large number of local minima, find energy barriers between them, and estimate local thermal averages over each basin of attraction. It is applied to the Sherrington-Kirkpatrick (SK) spin glass Hamiltonian where existing methods have difficulties even for a moderate number of spins. Finite-size results are used to make predictions in the thermodynamic limit that match theoretical approximations and recent findings on the free energy landscapes of SK spin glasses.     

Flowing crystals: nonequilibrium structure of foam

Bubbles pushed through a quasi-two-dimensional channel self-organize into a variety of periodic lattices. The structures of these lattices correspond to local minima of the interfacial energy. The "flowing crystals" are long-lived metastable states, a small subset of possible local minima of confined quasi-two-dimensional foams [P. Garstecki and G. M. Whitesides, Phys. Rev. E 73, 031603 (2006)10.1103/PhysRevE.73.031603]. Experimental results suggest that the choice of the structures that we observe is dictated by the dynamic stability of the cyclic processes of their formation. Thus, the dynamic system that we report provides a unique example of nonequilibrium self-organization that results in structures that correspond to local minima of the relevant energy functional.     

Ferromagnetism in the Hubbard model: Spin waves and instability of the Nagaoka state

We discuss two single spin flip variational wave functions describing spin wave excitations which were proposed earlier by Shastry, Krishnamurthy and Anderson (SKA) and by Basile and Elser (BE), respectively, in order to investigate the instability of the fully polarized ferromagnetic state (Nagaoka state) in the infinite U Hubbard model. We calculate the energy of these variational states for the square lattice and for multiple chains. At the zone boundary in the vicinity of the point (0, π) the spin wave energy is reduced substantially by the binding of the spin up hole to the flipped down spin. For the square lattice this leads to a critical hole density of δ_cr = 0.407 for the SKA spin wave and of δ_cr = 0.322 for the BE spin wave which implies remarkable improvements in comparison to the corresponding scattering states investigated previously.