2014 We continue and improve the transfer matrix approach of Derrida and de Seze by incorporating in two different ways the leading corrections to the asymptotic behaviour for wide strips. We find for the site percolation threshold in the square lattice pc = 0.59274 ± 0.00010, for the radius exponent of lattice animals 0.64075 ± 0.00015, and for the inverse growth factor or critical fugacity 0....

Self-avoiding random surfaces on a cubic lattice are studied by extensive Monte Carlo sampling. The surfaces have empty boundary and the topology of a 2-sphere. An oct-tree data-structure allows to obtain good statistics for surfaces whose plaquette number is almost an order of magnitude greater than in previous investigations. Maximum likelihood determinations of the critical plaquette fugacit...

We apply the Stein-Chen method for Poisson approximation to spin-half Isingtype models, in positive external eld, which satisfy the FKG inequality. In particular we show that, provided the density of minus spins is low and can be expanded as a convergent power series in the activity (fugacity) variable, the distribution of minus spins is approximately Poisson. The error of the approximation is ...

We review the overlap pathology of the Glasgow reweighting method for finite density QCD, and discuss the sampling bias that effects the determination of the ensemble-averaged fugacity polynomial expansion coefficients that form the Grand Canonical Partition function. The expectation of the difference in free energies between canonical partition functions generated with different measures is pr...

We give a sufficiently detailed account on the construction of marked Gibbs measures in the high temperature and low fugacity regime. This is proved for a wide class of underlying spaces and potentials such that stability and integrability conditions are satisfied. That is, for state space we take a locally compact separable metric space X and a separable metric space S for the mark space. This...

The goal of this study was to use the modeling tools for prediction of environmental concentrations and pools of pesticides (HCB and DDT) in soil. The characterization and quantification of secondary background sources of HCB, were computed using fugacity based deterministic model. Areas with a high potential for deposition and volatilization of HCB were identified. Results of modeling were map...

In a simplified model we study the hadronization of quark matter in an expanding fireball, in particular the approach to a final hadronic composition in equilibrium. Ideal hadron gas equilibrium constrained by conservation laws, the fugacity parametrization, as well as linear and non-linear coalescence approaches are recognized as different approximations to this in-medium quark fusion process....

Glauber dynamics is a powerful tool to generate randomized, approximate solutions to combinatorially difficult problems. Applications include Markov Chain Monte Carlo (MCMC) simulation and distributed scheduling for wireless networks. In this paper, we derive bounds on the mixing time of a generalization of Glauber dynamics where multiple vertices are allowed to update their states in parallel ...

We investigate hexatic membranes embedded in Euclidean D-dimensional space using a reparametrization invariant formulation combined with exact renormalization group equations. An XY model coupled to a fluid membrane, when integrated out, induces long-range interactions between curvatures described by a Polyakov term in the effective action. We evaluate the contributions of this term to the runn...

A Hamiltonian cycle of a graph is a closed path that visits every vertex once and only once. It serves as a model of a compact polymer on a lattice. I study the number of Hamiltonian cycles, or equivalently the entropy of a compact polymer, on various lattices that are not necessarily homogeneous. Estimates for the number are obtained by two methods. One is the saddle point approximation for a ...