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

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

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

Speeding Up Computer Simulations: The Transition Observable Method

A method is presented which allows for a tremendous speed-up of computer simulations of statistical systems by orders of magnitude. This speed-up is achieved by means of a new observable, while the algorithm of the simulation remains unchanged.Comment: 20 pages, 6 figures Submitted to Phys.Rev.E (August 1999) Replacement due to some minor change

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.

Finite size effects and the order of a phase transition in fragmenting nuclear systems

We discuss the implications of finite size effects on the determination of the order of a phase transition which may occur in infinite systems. We introduce a specific model to which we apply different tests. They are aimed to characterise the smoothed transition observed in a finite system. We show that the microcanonical ensemble may be a useful framework for the determination of the nature of such transitions.Comment: LateX, 5 pages, 5 figures; Fig. 1 change

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]

Effective charge-spin models for quantum dots

It is shown that at low densities, quantum dots with few electrons may be mapped onto effective charge-spin models for the low-energy eigenstates. This is justified by defining a lattice model based on a many-electron pocket-state basis in which electrons are localised near their classical ground-state positions. The equivalence to a single-band Hubbard model is then established leading to a charge-spin ($t-J-V$) model which for most geometries reduces to a spin (Heisenberg) model. The method is refined to include processes which involve cyclic rotations of a ``ring'' of neighboring electrons. This is achieved by introducing intermediate lattice points and the importance of ring processes relative to pair-exchange processes is investigated using high-order degenerate perturbation theory and the WKB approximation. The energy spectra are computed from the effective models for specific cases and compared with exact results and other approximation methods.Comment: RevTex, 24 pages, 7 figures submitted as compressed and PostScript file

A Method to Study Relaxation of Metastable Phases: Macroscopic Mean-Field Dynamics

We propose two different macroscopic dynamics to describe the decay of metastable phases in many-particle systems with local interactions. These dynamics depend on the macroscopic order parameter $m$ through the restricted free energy $F(m)$ and are designed to give the correct equilibrium distribution for $m$. The connection between macroscopic dynamics and the underlying microscopic dynamic are considered in the context of a projection- operator formalism. Application to the square-lattice nearest-neighbor Ising ferromagnet gives good agreement with droplet theory and Monte Carlo simulations of the underlying microscopic dynamic. This includes quantitative agreement for the exponential dependence of the lifetime on the inverse of the applied field $H$, and the observation of distinct field regions in which the derivative of the lifetime with respect to $1/H$ depends differently on $H$. In addition, at very low temperatures we observe oscillatory behavior of this derivative with respect to $H$, due to the discreteness of the lattice and in agreement with rigorous results. Similarities and differences between this work and earlier works on finite Ising models in the fixed-magnetization ensemble are discussed.Comment: 44 pages RevTeX3, 11 uuencoded Postscript figs. in separate file