Modelling of a displacive transformation in two-dimensional system within four-body approximation of Continuous Displacement Cluster Variation Method

Following our previous study on distorted to non-distorted displacive phase transformation in the two-dimensional square lattice based on the continuous displacement cluster variation method (CDCVM) within the Bragg–Williams (BW) approximation, we performed a higher order approximation, four-body approximation, in the entropy term and compared the results obtained by the two approximations. The transformation temperature decreases with the higher order approximation, which shares the common feature with conventional CVM studies on replacive transformations. The present study predicts the first-order transformation, which is markedly different from the previous study based on the BW approximation. Furthermore, by employing the four-body approximation, we are able to reproduce the o-type distribution of displaced atoms around a Bravais lattice point by changing the atomic interaction energy, which was by no means possible by the BW approximation.     

Monte Carlo calculation of the configurational entropy and combinatory factor on binary alloys

A method is presented for the calculation of free energy and entropy of regular solutions. It is based on a calculation of the configurational density of states (combinatory factor), from Monte Carlo computations. Application to the planar square lattice shows an excellent agreement with exact results. Results on a bcc lattice are presented.     

Magnetism and pairing of two-dimensional trapped fermions

The emergence of local phases in a trapped two-component Fermi gas in an optical lattice is studied using quantum Monte Carlo simulations. We treat temperatures that are comparable to or lower than those presently achievable in experiments and large enough systems that both magnetic and paired phases can be detected by inspection of the behavior of suitable short-range correlations. We use the latter to suggest the interaction strength and temperature range at which experimental observation of incipient magnetism and d-wave pairing are more likely and evaluate the relation between entropy and temperature in two-dimensional confined fermionic systems.     

Free fermion propagators and lattice finite-size effects

Efficient methods are described for calculating the various “hadron” (fermion bilinear/trilinear) propagators for free lattice fermions. For lattice sizes typical of current Monte Carlo calculations, the large finite-size effects are investigated. Periodic and antiperiodic boundary conditions in the spatial directions appear to yield upper and lower bounds respectively for both the meson-like and baryon-like propagators.     

Vibrational contribution to the thermodynamics of nanosized precipitates: vacancy-copper clusters in bcc-Fe

The effects of lattice vibration on the thermodynamics of nanosized coherent clusters in bcc-Fe consisting of vacancies and/or copper are investigated within the harmonic approximation. A combination of on-lattice simulated annealing based on Metropolis Monte Carlo simulations and off-lattice relaxation by molecular dynamics is applied to obtain the most stable cluster configurations at T = 0 K. The most recent interatomic potential built within the framework of the embedded-atom method for the Fe-Cu system is used. The total free energy of pure bcc-Fe and fcc-Cu as well as the total formation free energy and the total binding free energy of the vacancy-copper clusters are determined for finite temperatures. Our results are compared with the available data from previous investigations performed using many-body interatomic potentials and first-principles methods. For further applications in rate theory and object kinetic Monte Carlo simulations, the vibrational effects evaluated in the present study are included in the previously developed analytical fitting formulae.     

Markov entropy decomposition: a variational dual for quantum belief propagation

We present a lower bound for the free energy of a quantum many-body system at finite temperature. This lower bound is expressed as a convex optimization problem with linear constraints, and is derived using strong subadditivity of von Neumann entropy and a relaxation of the consistency condition of local density operators. The dual to this minimization problem leads to a set of quantum belief propagation equations, thus providing a firm theoretical foundation to that approach. The minimization problem is numerically tractable, and we find good agreement with quantum Monte Carlo calculations for spin-1/2 Heisenberg antiferromagnet in two dimensions. This lower bound complements other variational upper bounds. We discuss applications to Hamiltonian complexity theory and give a generalization of the structure theorem of [P. Hayden et al., Commun. Math. Phys. 246, 359 (2004).] to trees in an appendix.     

Monte Carlo simulations including energy from an entropic force

Several experimental techniques have shown that the primary response of many materials comes from a heterogeneous distribution of independently relaxing nanoscale regions; but most Monte Carlo simulations have homogeneous correlations. Resolving this discrepancy may require including the energy needed to change the configurational entropy, which is often used in theoretical treatments of thermal fluctuations, but not in computer simulations. Here the local configurational entropy is shown to give a nonlinear correction to the Metropolis algorithm that restores conservation of energy, maintains maximum entropy, and yields heterogeneous correlations. The nonlinear correction also improves agreement between Monte Carlo simulations of the Ising model and measurements of specific heat and structural correlations from the Jahn–Teller distortion in LaMnO₃.     

Multicanonical chain-growth algorithm

We present a temperature-independent Monte Carlo method for the determination of the density of states of lattice proteins that combines the fast ground-state search strategy of the new pruned-enriched Rosenbluth chain-growth method and multicanonical reweighting for sampling the complete energy space. Since the density of states contains all energetic information of a statistical system, we can directly calculate the mean energy, specific heat, Helmholtz free energy, and entropy for all temperatures. We apply this method to lattice proteins consisting of hydrophobic and polar monomers, and for the examples of sequences considered, we identify the transitions between native, globule, and random coil states. Since no special properties of heteropolymers are involved in this algorithm, the method applies to polymer models as well.     

Finite-size effects for phase segregation in a two-dimensional asymmetric exclusion model with two species

We investigate the stationary states of a two-dimensional lattice gas model with exclusion, in the presence of an external field. The lattice is populated by equal numbers of positively and negatively charged particles. An analytical mean-field approach and Monte Carlo simulations give strong evidence of the fact that at any finite density the only relevant stationary state of the system in the thermodynamic limit is inhomogeneous, consisting of a strip of particles transverse to the field. In the inhomogeneous phase, the density profiles and the current measured by Monte Carlo simulations are closely related to those found in mean field. The same is true for the finite-size behavior of the system.     

Nonequilibrium wetting transition in a nonthermal 2D Ising model

Nonequilibrium wetting transitions are observed in Monte Carlo simulations of a kinetic spin system in the absence of a detailed balance condition with respect to an energy functional. A nonthermal model is proposed starting from a two-dimensional Ising spin lattice at zero temperature with two boundaries subject to opposing surface fields. Local spin excitations are only allowed by absorbing an energy quantum (photon) below a cutoff energy E _c . Local spin relaxation takes place by emitting a photon which leaves the lattice. Using Monte Carlo simulation nonequilibrium critical wetting transitions are observed as well as nonequilibrium first-order wetting phenomena, respectively in the absence or presence of absorbing states of the spin system. The transitions are identified from the behavior of the probability distribution of a suitably chosen order parameter that was proven useful for studying wetting in the (thermal) Ising model.     

Lattice-gas model driven by Hubbard electrons

Self-consistent Monte Carlo simulations are undertaken for a lattice-gas model which is driven by the free energy of electrons described by a Hubbard model with electronic hopping restricted to ions at nearest-neighbor sites. Our previous work, an independent-electron tight-binding lattice-gas model (bcc or fcc), is modified to introduce two effects: the disorder of the dense system and, more importantly, the role of the electronic correlation. The first effect is achieved using an fcc lattice, but restricted so an occupied site can have no more than eight, instead of twelve, occupied nearest-neighbor sites. To treat correlations, the electronic intra-atomic repulsion is, at first, included via the Gutzwiller approximation at finite temperature; this approach is simple enough to be solved for all cases in the large, disordered systems used in our Monte Carlo simulations but can still give a good qualitative representation of the main effects of the electronic correlations. Then, the exact treatment of the Hubbard model for clusters with up to six atoms is integrated into the calculation. We obtain vapor-liquid coexistence curves and then, approximations to the electronic conductivities and paramagnetic susceptibilities at coexistence conditions. This simple model is, in part, motivated by experiments on the alkali-metal fluids.     

Nonextensive entropy and the non-Gaussian distribution of magnetization in two-dimensional spin ice

The statistical properties of the magnetization of the finite clusters of two-dimensional spin ice have been investigated. It has been shown by Monte Carlo simulations that the short-range ice rules in two dimensions lead to long-range correlations, which decay by a power law with distance. The long-range correlations, in turn, cause the nonextensivity of entropy and inapplicability of the central limit theorem for the magnetization. The behavior of the moments and distribution function of the magnetization with the cluster size disagrees with the theoretical predictions of the dipolar behavior of the correlation functions in two-dimensional spin ice.     

Two-stage ordering of spins in dipolar spin ice on the kagome lattice

Spin ice, a peculiar thermal state of a frustrated ferromagnet on the pyrochlore lattice, has a finite entropy density and excitations carrying magnetic charge. By combining analytical arguments and Monte Carlo simulations, we show that spin ice on the two-dimensional kagome lattice orders in two stages. The intermediate phase has ordered magnetic charges and is separated from the paramagnetic phase by an Ising transition. The transition to the low-temperature phase is of the three-state Potts or Kosterlitz-Thouless type, depending on the presence of defects in the charge order.     

Monte Carlo study of the Quartet Ising model consistent with selfduality

The transition temperature obtained from recent Monte Carlo calculations for the Quartet Ising model on the fcc lattice deviated by 17% from the exact transition temperatureT _c ^SD required by selfduality which we have proven afterwards. Here we use Monte Carlo results of the internal energy, which agree well with low- and high temperature series, to determine entropy and free energy and obtain aT _c in excellent agreement (±0.1%) with the exact value. The Quartet model on the hcp lattice is shown to be selfdual too; the rapidly converging series for the fcc and the hcp lattice differ only in higher order.Guest stay     

The self-consistent diagram approximation for lattice systems

We apply the self-consistent diagram approximation to calculate equilibrium properties of lattice systems. The free energy of the system is represented by a diagram expansion in Mayer-like functions with averaging over states of a reference system. The latter is defined by one-particle mean potentials, which are calculated using the variational condition formulated. As an example, numerical computations for a two-dimensional lattice gas on a square lattice with attractive interaction between nearest neighbours were carried out. The critical temperature, the phase coexistence curve, the chemical potential and particle and vacancy distribution functions coincide within a few per cent with exact or with Monte Carlo data. Received 18 March 1999 and Received in final form 8 November 1999     

SCDA for 3D lattice gases with repulsive interaction

The selfconsistent diagram approximation (SCDA) is generalized for three-dimensional lattice gases with nearest neighbor repulsive interactions. The free energy is represented in a closed form through elementary functions. Thermodynamical (phase diagrams, chemical potential and mean square fluctuations), structural (order parameter, distribution functions) as well as diffusional characteristics are investigated. The calculation results are compared with the Monte Carlo simulation data to demonstrate high precision of the SCDA in reproducing the equilibrium lattice gas characteristics. It is shown that similarly to two-dimensional systems the specific statistical memory effects strongly influence the lattice gas diffusion in the ordered states. Received 7 August 2002 / Received in final form 22 January 2003 Published online 24 April 2003     

Phase transitions of the energy-relative enstrophy theory for a coupled barotropic fluid–rotating sphere system

The statistical equilibrium of a coupled barotropic fluid–rotating solid sphere system is simulated using a energy-relative enstrophy spherical model in a wide range of parameter space by Monte Carlo (MC) methods [J.M. Hammersley, D.C. Handscomb, Monte Carlo Methods, Methuen & Co, London, Wiley, New York City, 1964; C.C. Lim, J. Nebus, Vorticity, Statistical Mechanics and Simulations, Springer, Berlin, 2006]. The energy-relative enstrophy model does not have the low temperature defect of the classical energy–enstrophy theory [R.H. Kraichnan, Statistical dynamics of two-dimensional flows, J. Fluid Mech. 67 (1975) 155–175] because of its microcanonical constraint on relative enstrophy. This model also differs from previous work in not fixing the angular momentum. A family of spin–lattice models are derived as convergent finite dimensional approximations to the total kinetic energy. MC simulations are used to calculate the mean nearest neighbor parity as order parameter or indicator of phase transitions in the system.     

Thermodynamics predicts how confinement modifies the dynamics of the equilibrium hard-sphere fluid

We study how confining the equilibrium hard-sphere fluid to restrictive one- and two-dimensional channels with smooth interacting walls modifies its structure, dynamics, and entropy using molecular dynamics and transition-matrix Monte Carlo simulations. Although confinement strongly affects local structuring, the relationships between self-diffusivity, excess entropy, and average fluid density are, to an excellent approximation, independent of channel width or particle-wall interactions. Thus, thermodynamics can be used to predict how confinement impacts dynamics.