We derive the exact general form of the equation of state, in the fugacity format, for the two-dimensional Coulomb gas. Our results are valid in the conducting phase of the Coulomb gas, for temperatures above the Kosterlitz-Thouless transition. The derivation of the equation of state is based on the knowledge of the general form of the short-distance expansion of the correlation functions of th...

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...