Exact partition function and boundary state of 2D massive Ising field theory with boundary magnetic field

We compute the exact partition function, the universal ground-state degeneracy and boundary state of the 2D Ising model with boundary magnetic field at off-critical temperatures. The model has a domain that exhibits states localized near the boundaries. We study this domain of boundary bound state and derive exact expressions for the “g function” and boundary state for all temperatures and boundary magnetic fields. In the massless limit we recover the boundary renormalization group flow between the conformally invariant free and fixed boundary conditions.     

The stationary state and the heat equation for a variant of Davies' model of heat conduction

We study a variant of Davies' model of heat conduction, consisting of a chain of (classical or quantum) harmonic oscillators, whose ends are coupled to thermal reservoirs at different temperatures, and where neighboring oscillators interact via intermediate reservoirs. In the weak coupling limit, we show that a unique stationary state exists, and that a discretized heat equation holds. We give an explicit expression of the stationary state in the case of two classical oscillators. The heat equation is obtained in the hydrodynamic limit, and it is proved that it completely describes the macroscopic behavior of the model.     

A scenario for the electronic state in the manganese perovskites: the orbital correlated metal

We propose a novel scenario for the electronic state in the manganese perovskites. We argue that, at low temperatures and within the ferromagnetic state, the physics of these colossal magnetoresistance compounds may be characterized by a correlated metallic state near a metal insulator transition where the orbital degrees of freedom play the main role. This follows from the observation that a two-band degenerate Hubbard model under a strong magnetic field can be mapped onto a para-orbital single band model. We solve the model numerically using the quantum Monte-Carlo technique within a dynamical mean field theory which is exact in the limit of large lattice connectivity. We argue that the proposed scenario may allow for the qualitative interpretation of a variety of experiments which were also observed in other (early) transition metal oxides. Received: 3 October 1997 / Revised: 9 December 1997 / Accepted: 12 January 1998     

The one-dimensional long-range ferromagnetic Ising model with a periodic external field

We consider the one-dimensional ferromagnetic Ising model with very long-range interaction under a periodic, biased and weak external field and prove that at sufficiently low temperatures the model has a unique limiting Gibbs state.     

Imaging cluster surfaces with atomic resolution: the strong metal-support interaction state of Pt supported on TiO2(110)

Nanosized platinum clusters were grown on a TiO2(110) surface and annealed in ultrahigh vacuum at high temperatures. This leads to the so-called strong metal-support interaction (SMSI) state, characterized by a complete encapsulation of the clusters with a reduced titanium oxide layer. We present atomically resolved scanning tunneling microscopy measurements of the cluster surfaces and an atomic model of the SMSI state. The ability to resolve the cluster surface geometry with atomistic detail may help to identify the active sites responsible for the SMSI.     

Direct observation of dark exciton states in single carbon nanotubes

We have studied magneto-photoluminescence (PL) spectra of a single carbon nanotube at low temperatures. A single PL peak arising from optically allowed (bright) exciton state was observed under the zero-magnetic field, and an additional PL peak from optically forbidden (dark) exciton state was enhanced with increasing the magnetic field. Excitons populate in the lower dark state at low temperatures, and the optically forbidden transition is observed due to the Aharonov-Bohm effect.     

Superfluid phase transition in two-dimensional excitonic systems

We study the superfluid phase transition in the two-dimensional (2D) excitonic system. Employing the extended Falicov–Kimball model (EFKM) and considering the local quantum correlations in the system composed of conduction band electrons and valence band holes we demonstrate the existence of the excitonic insulator (EI) state in the system. We show that at very low temperatures, the particle phase stiffness in the pure-2D excitonic system, governed by the non-local cross correlations, is responsible for the vortex–antivortex binding phase-field state, known as the Berezinskii–Kosterlitz–Thouless (BKT) superfluid state. We demonstrate that the existence of excitonic insulator phase is a necessary prerequisite, leading to quasi-long-range order in the 2D excitonic system.     

Entropy Production in Nonlinear,Thermally Driven Hamiltonian Systems

We consider a finite chain of nonlinear oscillators coupled at its ends to two infinite heat baths which are at different temperatures. Using our earlier results about the existence of a stationary state, we show rigorously that for arbitrary temperature differences and arbitrary couplings, such a system has a unique stationary state. (This extends our earlier results for small temperature differences.) In all these cases, any initial state will converge (at an unknown rate) to the stationary state. We show that this stationary state continually produces entropy. The rate of entropy production is strictly negative when the temperatures are unequal and is proportional to the mean energy flux through the system     

Statistics of a hydrophobic chain near a hydrophobic boundary

We study the behavior of a hydrophobic chain near a hydrophobic boundary in two dimensions, adapting the decorated lattice model of Berkema and Widom (G.T. Barkema, B. Widom, J. Chem. Phys. 113, 2349 (2000)) to obtain effective, temperature-dependent intrachain and chain-boundary interactions. We use these interactions to construct two model Hamiltonians. The resulting partition functions may be integrated numerically. Our results compare favorably with preliminary Monte Carlo computations, using the same effective interactions. At relatively low temperatures and at high temperatures, we find that the chain is randomly configured in the ambient water, and detached from the wall, whereas at intermediate temperatures it adsorbs onto the wall in a stretched or partially folded state, again depending upon the temperature, and the energy of solvation.     

Quarkonium spectral functions with complex potential

We study quarkonium spectral functions at high temperatures using a potential model with complex potential. The real part of the potential is constrained by the lattice QCD data on static quark anti-quark correlation functions, while the imaginary part of the potential is taken from perturbative calculations. We find that the imaginary part of the potential has significant effect on quarkonium spectral functions, in particular, it leads to the dissolution of the 1S charmonium and excited bottomonium states at temperatures about 250 MeV and melting of the ground state bottomonium at temperatures slightly above 450 MeV.     

Refining the spin Hamiltonian in the spin-1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2 using single crystals

We report thermodynamic measurements of the S=1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2, a promising candidate system with a spin-liquid ground state. Using single crystal samples, the magnetic susceptibility both perpendicular and parallel to the kagome plane has been measured. A small, temperature-dependent anisotropy has been observed, where χ(z)/χ(p)>1 at high temperatures and χ(z)/χ(p)<1 at low temperatures. Fits of the high-temperature data to a Curie-Weiss model also reveal an anisotropy. By comparing with theoretical calculations, the presence of a small easy-axis exchange anisotropy can be deduced as the primary perturbation to the dominant Heisenberg nearest neighbor interaction. These results have great bearing on the interpretation of theoretical calculations based on the kagome Heisenberg antiferromagnet model to the experiments on ZnCu3(OH)6Cl2.     

Competition between crystalline electric field singlet and itinerant states of f electrons

A new kind of phase transition is proposed for lattice fermion systems with simplified f ² configurations at each site. The free energy of the model is computed in the mean-field approximation for both the itinerant state with the Kondo screening, and a localized state with the crystalline electric field (CEF) singlet at each site. The presence of a first-order phase transition is demonstrated in which the itinerant state changes into the localized state toward lower temperatures. In the half-filled case, the insulating state at high temperatures changes into a metallic state, in marked contrast with the Mott transition in the Hubbard model. For comparison, corresponding states are discussed for the twoimpurity Kondo system with f ¹ configuration at each site.     

Modelling Quasicrystals at Positive Temperature

We consider a two-dimensional lattice model of equilibrium statistical mechanics, using nearest neighbor interactions based on the matching conditions for an aperiodic set of 16 Wang tiles. This model has uncountably many ground state configurations, all of which are nonperiodic. The question addressed in this paper is whether nonperiodicity persists at low but positive temperature. We present arguments, mostly numerical, that this is indeed the case. In particular, we define an appropriate order parameter, prove that it is identically zero at high temperatures, and show by Monte Carlo simulation that it is nonzero at low temperatures.     

First-principles based atomistic modeling of phase stability in PMN-xPT

We have performed molecular dynamics simulations using a shell model potential developed by fitting first-principles results to describe the behavior of the relaxor-ferroelectric (1 - x)PbMg(1/3)Nb(2/3)O(3)-xPbTiO(3) (PMN-xPT) as a function of concentration and temperature, using site occupancies within the random site model. In our simulations, PMN is cubic at all temperatures and behaves as a polar glass. As a small amount of Ti is added, a weak polar state develops, but structural disorder dominates, and the symmetry is rhombohedral. As more Ti is added the ground state is clearly polar and the system is ferroelectric, but with easy rotation of the polarization direction. In the high Ti content region, the solid solution adopts ferroelectric behavior similar to PT, with tetragonal symmetry. The ground state sequence with increasing Ti content is R-M(B)-O-M(C)-T. The high-temperature phase is cubic at all compositions. Our simulations give the slopes of the morphotropic phase boundaries, crucial for high-temperature applications. We find that the phase diagram of PMN-xPT can be understood within the random site model.     

Spin waves,vortices, and the structure of equilibrium states in the classicalXY model

We prove that, for spin systems with a continuous symmetry group on lattices of arbitrary dimension, the surface tension vanishes at all temperatures. For the classicalXY model in zero magnetic field, this result is shown to imply absence of interfaces in the thermodynamic limit, at arbitrary temperature. We show that, at values of the temperature at which the free energy of that model is continuously differentiable, i.e. at all except possibly countably many temperatures, there iseither aunique translation-invariant equilibrium state, or all such states are labelled by the elements of the symmetry group, SO(2). Moreover, there areno non-translation-invariant, but periodic equilibrium states. We also reconsider the representation of theXY model as a gas of spin waves and vortices and discuss the possibility that, in four or more dimensions, translation invariance may be broken by imposing boundary conditions which force an (open) vortex sheet through the system. Among our main tools are new correlation inequalities.     

A model of heat conduction

We construct a model of a chain of atoms coupled at its ends to two reservoirs at different temperatures. In a weak coupling limit the atoms obey a stochastic evolution law and have an equilibrium state with a uniform temperature gradient along the chain.     

Isothermal compressibility and bulk modulus for methanol under the effect of pressure and temperatures

It has been demonstrated that the spinodal model produces very well the isothermal compressibility of liquid methanol for a wide range of pressures and temperatures. We have used the pseudospinodal model further to determine pressure derivatives, first-order as well as second-order of isothermal compressibility and bulk modulus for liquid methanol in the range of pressures (0–100 MPa) and temperatures (208.17 K–298.16 K). The results have been found to present close agreement with the available experimental data. We have also calculated the values of densities as a function of pressure and temperature for methanol using the Stacey equation of state.     

Quantum approach to classical statistical mechanics

We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.     

Phase diagram in the quantum XY model with long-range interactions

We study the d-dimensional quantum XY model with ferromagnetic long-range interaction decaying as r-p in terms of boson operators, by employing the coherent state path integral approach. We have obtained a finite critical temperature as a function of the dimension (d) for d2d the system becomes disordered at all temperatures. For the particular values p=3/2 and d=1 our theoretical calculations are comparable to those from Monte Carlo simulations.