Persistence distributions in a conserved lattice gas with absorbing states

Extensive simulations are performed to study the persistence behavior of a conserved lattice gas model exhibiting an absorbing phase transition from an active phase into an inactive phase. Both the global and the local persistence exponents are determined in two and higher dimensions. The local persistence exponent obeys a scaling relation involving the order parameter exponent of the absorbing phase transition. Furthermore we observe that the global persistence exponent exceeds its local counterpart in all dimensions in contrast to the known persistence behavior in reversible phase transitions. Received 27 August 2001 and Received in final form 15 November 2001     

Heat conduction in a two-dimensional Ising model

A cylindrical Ising model between thermostats is used to explore the heat conduction for any temperature interval. The standard Q2R and Creutz dynamics, previously used by Saito, Takesue and Miyashita, fail below the critical temperature, limiting the analysis to high temperatures intervals. We introduce improved dynamics by removing limitations due to the chessboard-like refresh, and by supplementing the Q2R rule with Kadanoff-Swift moves. These new dynamics not only prove highly efficient in recovering old results in their domains of validity, but also allow exploration of steady heat transport between two arbitrary temperatures, i.e. very far from equilibrium. From an ansatz avoiding references to quasi equilibrium or to local temperature, and from comparison with numerical simulations, we can consistently define a generalized diffusivity. Its dependence on the energy density may be evaluated without any recourse to the Green-Kubo formula.     

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     

The travelling salesman problem on randomly diluted lattices: Results for small-size systems

If one places N cities randomly on a lattice of size L, we find that and vary with the city concentration p=N/L ², where is the average optimal travel distance per city in the Euclidean metric and is the same in the Manhattan metric. We have studied such optimum tours for visiting all the cities using a branch and bound algorithm, giving the exact optimized tours for small system sizes () and near-optimal tours for bigger system sizes (). Extrapolating the results for , we find that for p=1, and and with as . Although the problem is trivial for p=1, for it certainly reduces to the standard travelling salesman problem on continuum which is NP-hard. We did not observe any irregular behaviour at any intermediate point. The crossover from the triviality to the NP-hard problem presumably occurs at p=1. Received 15 April 2000     

Persistence of opinion in the Sznajd consensus model: computer simulation

The density of never changed opinions during the Sznajd consensus-finding process decays with time t as 1/t ^θ. We find θ ≃ 3/8 for a chain, compatible with the exact Ising result of Derrida et al. In higher dimensions, however, the exponent differs from the Ising θ. With simultaneous updating of sublattices instead of the usual random sequential updating, the number of persistent opinions decays roughly exponentially. Some of the simulations used multi-spin coding. Received 22 August 2002 / Received in final form 12 November 2002 Published online 31 December 2002     

Spin glasses on Bethe lattices for large coordination number

We study spin glasses on random lattices with finite connectivity. In the infinite connectivity limit they reduce to the Sherrington Kirkpatrick model. In this paper we investigate the expansion around the high connectivity limit. Within the replica symmetry breaking scheme at two steps, we compute the free energy at the first order in the expansion in inverse powers of the average connectivity (z), both for the fixed connectivity and for the fluctuating connectivity random lattices. It is well known that the coefficient of the 1/z correction for the free energy is divergent at low temperatures if computed in the one step approximation. We find that this annoying divergence becomes much smaller if computed in the framework of the more accurate two steps breaking. Comparing the temperature dependance of the coefficients of this divergence in the replica symmetric, one step and two steps replica symmetry breaking, we conclude that this divergence is an artefact due to the use of a finite number of steps of replica symmetry breaking. The 1/z expansion is well defined also in the zero temperature limit. Received 15 July 2002 Published online 31 December 2002     

Ground state properties of a spin-3/2 model on a decorated square lattice

We present the construction of an optimum ground state for a quantum spin-3/2 antiferromagnet. The spins reside on a decorated square lattice, in which the basis consists of a plaquette of four sites. By using the vertex state model approach we generate the ground state from the same vertices as those used for the corresponding ground state on the hexagonal lattice. The properties of these two ground states are very similar. Particularly there is also a parameter-controlled phase transition from a disordered to a Néel ordered phase. In the regime of this transition, ground state properties can be obtained from an integrable classical vertex model. Received 28 June 1999     

Interactions of several replicas in the random field Ising model

The replicated field theory of the random field Ising model involves the couplings of replicas of different indices. The resulting correlation functions involve a superposition of different types of long distance behaviours. However the n = 0 limit allows one to discuss the renormalization group properties in spite of this phenomenon. The attraction of pairs of replicas is enhanced under renormalization flow and no stable fixed point is found. Consequently, an instability occurs in the paramagnetic region, before one reaches the Curie line, signalling the onset of replica symmetry breaking. Received 28 July 2000     

Ostwald ripening with kinetically limited bond formation

We present Monte Carlo simulations of the ripening of 2D islands in the case when the formation of the monomer-monomer bonds is kinetically limited. The results obtained indicate that such limitations may modify the early stage of the kinetics. Asymptotically, the ripening is described by the Lifshitz-Slyozov law. Received 29 August 2000     

Ground state phase diagram of a spin-2 antiferromagnet on the square lattice

We use the vertex state model approach to construct optimum ground states for a large class of quantum spin-2 antiferromagnets on the square lattice. Optimum ground states are exact ground states of the model which minimize all local interaction operators. The ground state contains two continuous parameters and exhibits a second order phase transition from a disordered phase with exponentially decaying correlation functions to a Néel ordered phase. The behaviour is very similar to that of the corresponding ground state of a quantum spin-3/2 model on the hexagonal lattice, which has been investigated in an earlier paper. Received 8 April 1999     

Universality in diffusion front growth dynamics

We have studied the scaling properties of diffusion fronts by numerical calculations based on the mean field approach in the context of a lattice gas model, performed in a triangular lattice. We find that the height-height correlation function scales with time t and length l as C(l, t) ≈l ^α f (t/l ^α/β) with α = 0.62±0.01 and β = 0.39±0.02. These exponent values are identical to those characterising the roughness of the diffusion fronts evolving through a square lattice [1,2], thus confirming their universality. Received 14 November 2001 / Received in final form 20 April 2002 Published online 31 July 2002     

Exact diagonalization of the S = 1/2 XY ferromagnet on finite bcc lattices to estimate T = 0 properties on the infinite lattice

In this paper finite bcc lattices are defined by a triple of vectors in two different ways - upper triangular lattice form and compact form. In Appendix A are lists of some 260 distinct and useful bcc lattices of 9 to 32 vertices. The energy and magnetization of the S = 1/2 XY ferromagnet have been computed on these bcc lattices in the lowest states for S _z = 0, 1/2, 1 and 3/2. These data are studied statistically to fit the first three terms of the appropriate finite lattice scaling equations. Our estimates of the T = 0 energy and magnetization agree very well with spin wave and series expansion estimates. Received 1st August 2000 and Received in final form 22 December 2000     

Ising magnets with mobile defects

Motivated by recent experiments on cuprates with low-dimensional magnetic interactions, a new class of two-dimensional Ising models with short-range interactions and mobile defects is introduced and studied. The non-magnetic defects form lines, which, as temperature increases, first meander and then become unstable. Using Monte Carlo simulations and analytical low- and high-temperature considerations, the instability of the defect stripes is monitored for various microscopic and thermodynamic quantities in detail for a minimal model, assuming some of the couplings to be indefinitely strong. The robustness of the findings against weakening the interactions is discussed as well. Received 22 August 2002 / Received in final form 4 October 2002 Published online 19 November 2002     

Excitation energy as a basic variable to control nuclear disassembly

Thermodynamical features of Xe system is investigated as functions of temperature and freeze-out density in the frame of lattice gas model. The calculation shows different temperature dependence of physical observables at different freeze-out density. In this case, the critical temperature when the phase transition takes place depends on the freeze-out density. However, a unique critical excitation energy %and the same excitation reveals regardless of freeze-out density when the excitation energy is used as a variable instead of temperature. Moreover, the different behavior of other physical observables with temperature due to different ρ_f vanishes when excitation energy replaces temperature. It indicates that the excitation energy can be seen as a more basic quantity to control nuclear disassembly. Received: 25 November 1998 /Revised version: 20 January 1999     

Condensation and metastability in the 2D Potts model

For the first order transition of the Ising model below , Isakov has proven that the free energy possesses an essential singularity in the applied field. Such a singularity in the control parameter, anticipated by condensation theory, is believed to be a generic feature of first order transitions, but too weak to be observable. We study these issues for the temperature driven transition of the q states 2D Potts model at . Adapting the droplet model to this case, we relate its parameters to the critical properties at and confront the free energy to the many informations brought by previous works. The essential singularity predicted at the transition temperature leads to observable effects in numerical data. On a finite lattice, a metastability domain of temperatures is identified, which shrinks to zero in the thermodynamical limit. Received 30 March 1999     

Election results and the Sznajd model on Barabasi network

The network of Barabasi and Albert, a preferential growth model where a new node is linked to the old ones with a probability proportional to their connectivity, is applied to Brazilian election results. The application of the Sznajd rule, that only agreeing pairs of people can convince their neighbours, gives a vote distribution in good agreement with reality Received 19 September 2001 and Received in final form 2 November 2001     

Dynamical invariants in the deterministic fixed-energy sandpile

The non-ergodic behavior of the deterministic Fixed Energy Sandpile (DFES), with Bak-Tang-Wiesenfeld (BTW) rule, is explained by the complete characterization of a class of dynamical invariants (or toppling invariants). The link between such constants of motion and the discrete Laplacians properties on graphs is algebraically and numerically clarified. In particular, it is possible to build up an explicit algorithm determining the complete set of independent toppling invariants. The partition of the configuration space into dynamically invariant sets, and the further refinement of such a partition into basins of attraction for orbits, are also studied. The total number of invariant sets equals the graphs complexity. In the case of two dimensional lattices, it is possible to estimate a very regular exponential growth of this number vs. the size. Looking at other features, the toppling invariants exhibit a highly irregular behavior. The usual constraint on the energy positiveness introduces a transition in the frozen phase. In correspondence to this transition, a dynamical crossover related to the halting times is observed. The analysis of the configuration space shows that the DFES has a different structure with respect to dissipative BTW and stochastic sandpiles models, supporting the conjecture that it lies in a distinct class of universality.     

Ionic diffusion on a lattice: Effects of the order-disorder transition on the dynamics of non-equilibrium systems

We examine the behaviour of the concentration profiles of particles with repulsive interactions diffusing on a host lattice. At low temperature, the diffusion process is strongly influenced by the presence of ordered domains. We use mean field equations and Monte-Carlo simulations to describe the various effects which influence the kinetic behaviour. An effective diffusion coefficient is determined analytically and is compared with the simulations. Finite gradient effects on the ordered domains and on the diffusion are discussed. The kinetics studied is relevant for superionic conductors, for intercalation and also for the diffusion of particles adsorbed on a substrate. Received: 26 June 1997 / Revised: 18 September 1997 / Accepted: 10 November 1997