Energy gap,clustering, and the Goldstone theorem in statistical mechanics

We prove a Goldstone-type theorem for a wide class of lattice and continuum quantum systems, both for the ground state and at nonzero temperature. For the ground state (T=0) spontaneous breakdown of a continuous symmetry implies no energy gap. For nonzero temperature, spontaneous symmetry breakdown implies slow clustering (noL ¹ clustering). The methods apply also to nonzero-temperature classical systems.Partial financial support by Fundação de Amparo à Pesquisa do Estado de São Paulo.Partial financial support by CNPq.     

Effect of magnetic field on dynamic response function in Ising systems

As a continuation of our previously published work, we use the Nelson?s method to study the effect of the magnetic field on the temperature-, frequency-, and momentum-dependent response function and dynamic correlation function in the Ising-type systems with relaxational dynamics. The scaling function is given within the renormalization group formalism at one-loop order for nonzero field. We show how the typical two-peak structure of the real part of response function changes with magnetic field. We discuss the deviations of the correlation function from the Gaussian expression. The Fisher–Langer maximum is also considered.     

Theoretical study of magnetic spin correlations and the magnetocapacitance effect in BiMnO<Subscript>3</Subscript>

The magnetic correlations between Mn ion spins and their effects on the magnetocapacitance in BiMnO₃ are studied based on a microscopic model. Above the phase transition temperature of the magnetic subsystem, the magnetic correlations including the longitudinal and transverse parts are nonzero, and they lead to a nonzero specific heat of magnetic subsystem. We show that the magnetocapacitance effect is ascribed to the fluctuation of magnetic correlation. The linear relation between electric susceptibility and the magnetic correlation is obtained and the relevant experiments are explained.     

Narrowing of topological bands due to electronic orbital degrees of freedom

The fractional quantum Hall effect has been predicted to occur in the absence of magnetic fields and at high temperature in lattice systems that have flat bands with a nonzero Chern number. We demonstrate that orbital degrees of freedom in frustrated lattice systems lead to a narrowing of topologically nontrivial bands. This robust effect does not rely on fine-tuned long-range hopping parameters and is directly relevant to a wide class of transition-metal compounds.     

Exchange monte carlo for molecular simulations with monoelectronic hamiltonians

We introduce a general Monte Carlo scheme for achieving atomistic simulations with monoelectronic Hamiltonians including the thermalization of both nuclear and electronic degrees of freedom. The kinetic Monte Carlo algorithm is used to obtain the exact occupation numbers of the electronic levels at canonical equilibrium, and comparison is made with Fermi-Dirac statistics in infinite and finite systems. The effects of a nonzero electronic temperature on the thermodynamic properties of liquid silver and sodium clusters are presented.     

Topological order at nonzero temperature

We propose a definition for topological order at nonzero temperature in analogy to the usual zero temperature definition that a state is topologically ordered, or "nontrivial", if it cannot be transformed into a product state (or a state close to a product state) using a local (or approximately local) quantum circuit. We prove that any two-dimensional Hamiltonian which is a sum of commuting local terms is not topologically ordered at T > 0. We show that such trivial states cannot be used to store quantum information using certain stringlike operators. This definition is not too restrictive, however, as the four dimensional toric code does have a nontrivial phase at nonzero temperature.     

Dynamics of a monodisperse Lennard-Jones system on a sphere

We investigate by molecular dynamics simulation a system of N particles moving on the surface of a two-dimensional sphere and interacting by a Lennard-Jones potential. We detail the way to account for the changes brought by a nonzero curvature, both at a methodological and at a physical level. When compared to a two-dimensional Lennard-Jones liquid on the Euclidean plane, where a phase transition to an ordered hexagonal phase takes place, we find that the presence of excess defects imposed by the topology of the sphere frustrates the hexagonal order. We observe at high density a rapid increase of the relaxation time when the temperature is decreased, whereas in the same range of temperature the pair correlation function of the system evolves only moderately.     

Possible evidence of a spontaneous spin polarization in mesoscopic two-dimensional electron systems

We have experimentally studied the nonequilibrium transport in low-density clean two-dimensional (2D) electron systems at mesoscopic length scales. At zero magnetic field (B), a double-peak structure in the nonlinear conductance was observed close to the Fermi energy in the localized regime. From the behavior of these peaks at nonzero B, we could associate them with the opposite spin states of the system, indicating a spontaneous spin polarization at B=0. Detailed temperature and disorder dependence of the structure shows that such a splitting is a ground-state property of low-density 2D systems.     

Creep of superconducting vortices in the limit of vanishing temperature: a fingerprint of off-equilibrium dynamics

We theoretically study the creep of vortex matter in superconductors. The low temperature experimental phenomenology, previously interpreted in terms of "quantum tunneling" of vortices, is reproduced by Monte Carlo simulations of a purely "classical" vortex model. We demonstrate that a nonzero creep rate in the limit of vanishing temperature is to be expected in systems with slow relaxations as a consequence of their off-equilibrium evolution in a complex free energy landscape.     

Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential

We analyze how individual eigenvalues of the QCD Dirac operator at nonzero quark chemical potential are distributed in the complex plane. Exact and approximate analytical results for both quenched and unquenched distributions are derived from non-Hermitian random matrix theory. When comparing these to quenched lattice QCD spectra close to the origin, excellent agreement is found for zero and nonzero topology at several values of the quark chemical potential. Our analytical results are also applicable to other physical systems in the same symmetry class.     

Boundary entropy of one-dimensional quantum systems at low temperature

The boundary beta function generates the renormalization group acting on the universality classes of one-dimensional quantum systems with boundary which are critical in the bulk but not critical at the boundary. We prove a gradient formula for the boundary beta function, expressing it as the gradient of the boundary entropy s at fixed nonzero temperature. The gradient formula implies that s decreases under renormalization, except at critical points (where it stays constant). At a critical point, the number exp((s) is the "ground-state degeneracy," g, of Affleck and Ludwig, so we have proved their long-standing conjecture that g decreases under renormalization, from critical point to critical point. The gradient formula also implies that s decreases with temperature, except at critical points, where it is independent of temperature. It remains open whether the boundary entropy is always bounded below.     

Fractionalization of angular momentum at finite temperature around a magnetic vortex

Ambiguities in the definition of angular momentum of a quantum-mechanical particle in the presence of a magnetic vortex are reviewed. We show that the long-standing problem of the adequate definition is resolved in the framework of the second-quantized theory at nonzero temperature. Planar relativistic Fermi gas in the background of a point-like magnetic vortex with arbitrary flux is considered, and we find thermal averages, quadratic fluctuations, and correlations of all observables, including angular momentum, in this system. The kinetic definition of angular momentum is picked out unambiguously by the requirement of plausible behaviour for the angular momentum fluctuation and its correlation with fermion number.     

The chiral phase transition at high baryon density from nonperturbative flow equations

We investigate the chiral phase transition at high baryon number density within the linear quark meson model for two flavors. The method we employ is based on an exact renormalization group equation for the free energy. Truncated nonperturbative flow equations are derived at nonzero chemical potential and temperature. Whereas the renormalization group flow leads to spontaneous chiral symmetry breaking in vacuum, we find a chiral symmetry restoring first order transition at high density. Combined with previous investigations at nonzero temperature, the result implies the presence of a tricritical point with long–range correlations in the phase diagram. Received: 24 August 1999 / Published online: 17 February 2000     

Signature of local motion in the microwave sky

For observers moving with respect to the cosmic rest frame, the microwave background temperature fluctuations will no longer be statistically isotropic. Aside from the familiar temperature dipole, an observer's velocity will also induce changes in the temperature angular correlation function and create nonzero off-diagonal correlations between multipole moments. We show that both of these effects should be detectable in future full-sky maps from the Planck satellite, and can constrain modifications of the standard cosmological model proposed to explain anomalous current observations.     

QCD thermodynamics from the lattice

We review the current methods and results of lattice simulations of quantum chromodynamics at nonzero temperatures and densities. The review is intended to introduce the subject to interested nonspecialists and beginners. It includes a brief overview of lattice gauge theory, a discussion of the determination of the crossover temperature, the QCD phase diagram at zero and nonzero densities, the equation of state, some in-medium properties of hadrons including charmonium, and some plasma transport coefficients.     

Intrinsic optical dichroism in the chiral superconducting state of Sr2RuO4

We present an analysis of the Hall conductivity σ(xy)(ω,T) in time reversal symmetry breaking states of exotic superconductors. We find that the dichroic signal is nonzero in systems with interband order parameters. This new intrinsic mechanism may explain the Kerr effect observed in strontium ruthenate and possibly other superconductors. We predict coherence factor effects in the temperature dependence of the imaginary part of the ac Hall conductivity Imσ(xy)(ω,T), which can be tested experimentally.     

Theoretical evidence for a reentrant phase diagram in ortho-para mixtures of solid H2 at 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.     

Classical one-dimensional Heisenberg model with an interaction of finite range

It is shown that the thermodynamic quantities and spin correlation functions of the classical Heisenberg model on a linear chain are expressed in terms of the eigenvalue with the smallest absolute value and the corresponding eigenfunction of a homogeneous linear integral equation, where the range of the interaction is assumed to be finite. The magnetization and susceptibility at nonzero external magnetic fields are given as a function of temperature, for the case of the nearest neighbour ferromagnetic and antiferromagnetic interaction. Efforts are paid to determine the properties near zero temperature.     

Temperature and the critical dimension of strings

Thermofield dynamics is used to generalize the BRST invariance of strings to nonzero temperature. The requirement that the BRST generator is nilpotent implies thatd=26 even at nonzero temperature.     

Particular features of a Vavilov-Cherenkov-like phenomenon with emission of surface plasmons

We consider a phenomenon of the Vavilov-Cherenkov type that can be observed in a space with a metal-dielectric boundary that well reflects light. An electron that initially uniformly moves at a constant velocity near this boundary creates surface plasmon-polaritons the phase velocity of which is lower than the electron velocity. The momentum of a photon in the created plasmon-polariton is calculated. This momentum may be almost as high as the doubled initial electron momentum. The velocity of the electron that created the photon in the plasmon-polariton may also become almost zero. We show that, at a nonzero temperature, this process has a nonzero probability.