Reconstruction of a first-order phase transition from computer simulations of individual phases and subphases

We present a new method for investigating first-order phase transitions using Monte Carlo simulations. It relies on the multiple-histogram method and uses solely histograms of individual phases. In addition, we extend the method to include histograms of subphases. The free energy difference between phases, necessary for attributing the correct statistical weights to the histograms, is determined by a detour in control parameter space via auxiliary systems with short relaxation times. We apply this method to a recently introduced model for structure formation in polypeptides for which other methods fail.Comment: 13 pages in preprint mode, REVTeX, 2 Figures available from the authors ([email protected], [email protected]

Theory of Distinct Crystal Structures of Polymerized Fullerides AC60, A=K, Rb, Cs: the Specific Role of Alkalis

The polymer phases of AC60 form distinct crystal structures characterized by the mutual orientations of the (C60-)n chains. We show that the direct electric quadrupole interaction between chains always favors the orthorhombic structure Pmnn with alternating chain orientations. However the specific quadrupolar polarizability of the alkali metal ions leads to an indirect interchain coupling which favors the monoclinic structure I2/m with equal chain orientations. The competition between direct and indirect interactions explains the structural difference between KC60 and RbC60, CsC60.Comment: 4 pages, 2 figures, 1 tabl

Symmetries of microcanonical entropy surfaces

Symmetry properties of the microcanonical entropy surface as a function of the energy and the order parameter are deduced from the invariance group of the Hamiltonian of the physical system. The consequences of these symmetries for the microcanonical order parameter in the high energy and in the low energy phases are investigated. In particular the breaking of the symmetry of the microcanonical entropy in the low energy regime is considered. The general statements are corroborated by investigations of various examples of classical spin systems.Comment: 15 pages, 5 figures include

Microcanonical entropy for small magnetisations

Physical quantities obtained from the microcanonical entropy surfaces of classical spin systems show typical features of phase transitions already in finite systems. It is demonstrated that the singular behaviour of the microcanonically defined order parameter and susceptibility can be understood from a Taylor expansion of the entropy surface. The general form of the expansion is determined from the symmetry properties of the microcanonical entropy function with respect to the order parameter. The general findings are investigated for the four-state vector Potts model as an example of a classical spin system.Comment: 15 pages, 7 figure

Kinetic effects in stimulated Brillouin scattering

The role of ion and electron kinetic effects in the nonlinear evolution of stimulated Brillouin scattering (SBS) is investigated by means of particle-in-cell numerical simulations. The simulations were carried out in one and two spatial dimensions (1D and 2D), with a full PIC code, in which both ions and electrons are kinetic. The full PIC simulations are compared with those obtained from a hybrid PIC code (kinetic ions and Boltzmann electrons), making it possible to determine in which limit the electron kinetic effects are important. The simulation geometry corresponds to a coherent laser beam interacting with an expanding plasma slab. In the 1D simulations, the interaction becomes incoherent, as time goes on, in a domain that spatially begins in the plasma region close to the laser light entrance, and that ends within the plasma at a frontier which moves faster than the ion acoustic wave (IAW) velocity. The higher the laser intensity, the faster moves the frontier of this spatial domain. The SBS reflectivity drops at the very moment when this domain fills entirely the plasma. Two regimes have to be distinguished. In the regimes of low laser intensity, strong sub-harmonic generation of the excited IAW is observed to take place in this moving spatial domain, so that the SBS reflectivity drop is interpreted as being due to sub-harmonic generation. In the opposite regime of high laser intensity, there is no evidence of strong sub-harmonic generation, whereas a strong ion heating is observed, so that the reflectivity drop is interpreted as being due to enhanced ion damping. In the 1D simulations the electron kinetic effects are found to be able to smooth temporally the SBS reflectivity, although the overall picture remains the same when the electrons are taken as a Boltzmann fluid. In the 2D simulations, the SBS reflectivity is observed to drop rapidly in time because of the efficient nonlinear Landau damping on the ions, as previously reported by Cohen et al. [1]. In these 2D simulations, the electron kinetic effects are found to play a negligible role as compared with the ion kinetic effects

Coulombically Interacting Electrons in a One-dimensional Quantum Dot

The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is investigated as a function of the electron number and of the system length. The limitations of a description in terms of a capacitance are demonstrated. The energetically lowest lying excitations are physically explained as vibrational and tunneling modes. The limits of a dilute, Wigner-type arrangement of the electrons, and a dense, more homogeneous charge distribution are discussed.Comment: 10 pages (excl. Figures), Figures added in POSTSCRIPT, LaTe

Inequivalence of ensembles in a system with long range interactions

We study the global phase diagram of the infinite range Blume-Emery-Griffiths model both in the canonical and in the microcanonical ensembles. The canonical phase diagram is known to exhibit first order and continuous transition lines separated by a tricritical point. We find that below the tricritical point, when the canonical transition is first order, the phase diagrams of the two ensembles disagree. In this region the microcanonical ensemble exhibits energy ranges with negative specific heat and temperature jumps at transition energies. These results can be extended to weakly decaying nonintegrable interactions.Comment: Revtex, 4 pages with 3 figures, submitted to Phys. Rev. Lett., e-mail [email protected]

Multicanonical Recursions

The problem of calculating multicanonical parameters recursively is discussed. I describe in detail a computational implementation which has worked reasonably well in practice.Comment: 23 pages, latex, 4 postscript figures included (uuencoded Z-compressed .tar file created by uufiles), figure file corrected

Finite-size behaviour of the microcanonical specific heat

For models which exhibit a continuous phase transition in the thermodynamic limit a numerical study of small systems reveals a non-monotonic behaviour of the microcanonical specific heat as a function of the system size. This is in contrast to a treatment in the canonical ensemble where the maximum of the specific heat increases monotonically with the size of the system. A phenomenological theory is developed which permits to describe this peculiar behaviour of the microcanonical specific heat and allows in principle the determination of microcanonical critical exponents.Comment: 15 pages, 7 figures, submitted to J. Phys.