Ramon Villanova

Three-dimensional 3-state Potts model revisited with new techniques

We report a fairly detailed finite-size scaling analysis of the first-order phase transition in the three-dimensional 3-state Potts model on cubic lattices with emphasis on recently introduced quantities whose infinite-volume extrapolations are governed only by exponentially small terms. In these quantities no asymptotic power series in the inverse volume are involved which complicate the finite-size scaling behaviour of standard observables related to the specific-heat maxima or Binder-parameter minima. Introduced initially for strong first-order phase transitions in q-state Potts models with “large enough” q, the new techniques prove to be surprisingly accurate for a q value as small as 3. On the basis of the high-precision Monte Carlo data of Alves et al. [Phys. Rev. B 43 (1991) 5846], this leads to a refined estimate of βt = 0.550 565(10) for the infinite-volume transition point.

Single-cluster Monte Carlo study of the Ising model on two-dimensional random lattices.

We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices with up to 80 000 sites which are linked together according to the Voronoi-Delaunay prescription. In one set of simulations we use reweighting techniques and finite-size scaling analysis to investigate the critical properties of the model in the very vicinity of the phase transition. In the other set of simulations we study the approach to criticality in the disordered phase, making use of improved estimators for measurements. From both sets of simulations we obtain clear evidence that the critical exponents agree with the exactly known exponents for regular lattices, i.e., that (lattice) universality holds for the two-dimensional Ising model.

Two-dimensional eight-state Potts model on random lattices: A Monte Carlo study

We use two-dimensional Poissonian random lattices of Voronoi/Delaunay type to study the effect of quenched coordination number randomness on the nature of the phase transition in the eight-state Potts model, which is of first order on regular lattices. From extensive Monte Carlo simulations we obtain strong evidence that the phase transition remains of first order for this type of quenched randomness. Our result is in striking contrast to a recent Monte Carlo study of quenched bond randomness for which the order of the phase transition changes from first to second order.

Ising model universality for two-dimensional lattices

Abstract We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices of Delaunay type with up to 80 000 sites. By applying reweighting techniques and finite-size scaling analyses to time-series data near criticality, we obtain unambiguous support that the critical exponents for the random lattice agree with the exactly known exponents for regular lattices, i.e., that (lattice) universality holds for the two-dimensional Ising model.

Ising model on three-dimensional random lattices: A Monte Carlo study

We report single-cluster Monte Carlo simulations of the Ising model on three-dimensional Poissonian random lattices with up to 128 00050 3 sites which are linked together according to the Voronoi-Delaunay prescription. For each lattice size quenched averages are performed over 96 realizations. By using reweighting techniques and finite-size scaling analyses we investigate the critical properties of the model in the close vicinity of the phase transition point. Our random lattice data provide strong evidence that, for the available system sizes, the resulting effective critical exponents are indistinguishable from recent high-precision estimates obtained in Monte Carlo studies of the Ising model and Φ 4 field theory on three-dimensional regular cubic lattices.

Spin models on random lattices

Under certain conditions phase transitions in systems with quenched disorder are expected to exhibit a different behaviour than in the corresponding pure system. Here we discuss a series of Monte Carlo studies of a special type of such disordered systems, namely spin models defined on quenched, random lattices exhibiting geometrical disorder in the connectivity of the lattice sites. In two dimensions we present results for the q-state Potts model on random tri-valent (Φ3) planar graphs, which appear quite naturally in the dynamically triangulated random surface (DTRS) approach to quantum gravity, as well as on Poissonian random lattices of Voronoi/Delaunay type. Both cases, q⩽4 and >4, are discussed which, in the pure model without disorder, give rise to second- and first-order phase transitions, respectively. In three dimensions results for the Ising model on Poissonian random lattices are briefly described. We conclude with a comparison of the two types of connectivity disorder with the more standard case of bond disorder, and a discussion of the distinguishing differences.

A non-quasi-competitive Cournot oligopoly with stability

This paper presents a classical Cournot oligopoly model with some peculiar features: it is non--quasi--competitive as price under N-poly is greater than monopoly price; Cournot equilibrium exists and is unique with each new entry; the successive equilibria after new entries are stable under the adjustment mechanism that assumes that actual output of each seller is adjusted proportionally to the difference between actual output and profit maximizing output. Moreover, the model tends to perfect competition as N goes to infinity, reaching the monopoly price again.

Environmental analysis of Wastewater Treatment Plants Control strategies

In this paper the environmental impacts of 10 control strategies implemented in the Benchmark Simulation Model No. 1 (BSM1) are evaluated by using Life Cycle Analysis (LCA). The aim is to analyze their environmental profiles in order to identify the main flows contributors to those impacts and to find the existing correlations between the control strategies and the selected impact categories. The knowledge of these correlations allows to assess where are located the main environmental impacts product of the plants operation under the control strategies evaluated and to take actions in order to reduce them.

Scaling laws for the two-dimensional eight-state Potts model with fixed boundary conditions

We study the effects of frozen boundaries in a Monte Carlo simulation near a first-order phase transition. Recent theoretical analysis of the dynamics of first-order phase transitions has enabled us to state the scaling laws governing the critical regime of the transition. We check these new scaling laws performing a Monte Carlo simulation of the two-dimensional, eight-state spin Potts model. In particular, our results support a pseudocritical

Finite-size analysis of the 4D abelian surface gauge model

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