arXiv subjects

J. F. Fernandez

Publications and source records attributed to J. F. Fernandez.

21 records · Page 2Linked to original sources

arXiv2000

Ordering of dipolar Ising crystals

We study Ising systems of spins with dipolar interactions. We find a simple approximate relation for the interaction energy between pairs of parallel lattice columns of spins running along the Ising spin direction. This relation provides insight into the relation between lattice geometry and the nature of the ordered state. It can be used to calculate ground state energies. We have also obtained ground state energies and ordering temperatures T_0 from Monte Carlo simulations. Simple empirical relations, that give T_0 for simple and body centered tetragonal lattices in terms of lattice parameters are also established. Finally, the nature of the ordered state and T_0 are determined for Fe_8 clusters, which crystallize on a triclinic lattice.

cond-mat.stat-mech↗

arXiv1999

Algorithm for normal random numbers

We propose a simple algorithm for generating normally distributed pseudo random numbers. The algorithm simulates N molecules that exchange energy among themselves following a simple stochastic rule. We prove that the system is ergodic, and that a Maxwell like distribution that may be used as a source of normally distributed random deviates follows when N tends to infinity. The algorithm passes various performance tests, including Monte Carlo simulation of a finite 2D Ising model using Wolff's algorithm. It only requires four simple lines of computer code, and is approximately ten times faster than the Box-Muller algorithm.

cond-mat↗

arXiv1998

Van der Waals loops and the melting transition in two dimensions

Evidence for the existence of van der Waals loops in pressure p versus volume v plots has for some time supported the belief that melting in two dimensions is a first order phase transition. We report rather accurate equilibrium p(v) curves for systems of hard disks obtained from long Monte Carlo simulations. These curves, obtained in the constant volume ensemble, using periodic boundary conditions, exhibit well defined van der Waals loops. We illustrate their existence for finite systems that are known to undergo a continuous transition in the thermodynamic limit. To this end, we obtain magnetization m versus applied field curves from Monte Carlo simulations of the 2D Ising model, in the constant m ensemble, at the critical point. Whether van der Waals loops for disk systems behave in the thermodynamic limit as they do for the 2D Ising model at the critical point cannot be ruled out. Thus, the often made claim that melting in 2D is a first order phase transition, based on the evidence that van der Waals loops exist, is not sound.

cond-mat.stat-mech↗